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What was the initial velocity of the second stone? If the total time the ball is in sight is 1. On doubling his speed he finds that it appears to blow from the southwest. Find the magnitude and direction of the wind's velocity. When it crosses a platform, it has acquired a velocity u. At this instant a bolt drops from the top of the elevator. Find the time for the bolt to hit the floor of the elevator.
The car is 10 m behind the truck. Two seconds later the driver of the car applies his brakes and just manages to avoid a rear-end collision.
Determine the constant rate at which the car decelerated. How long does it take the packet to reach the ground? Motion in Resisting Medium 1. In the presence of heavy air resistance the time of ascent t 1 is no longer equal to the time of descent t 2. Similarly the initial speed u with which the body is thrown is not equal to the final speed v with which the object returns. Determine the height to which the body will rise. Motion in Two Dimensions1. Find the time when the velocity vectors are perpendicular to each other and the distance of separation at that instant.
It then comes down and recrosses the top of the tower in time t 2 , time being measured from the instant the object was projected up. A second object released from the top of the tower reaches the ground in time t 3. It just clears three walls, the successive distances between them being r and 2r. The total horizontal range is nr, where n is an integer. Find n. If the boy stands at a distance of 5 m in front of the house and the house is 6 m deep and if the opening in the front window is 5 m above him and that in the back window 2 m higher, calculate the velocity and the angle of projection of the ball that will enable him to accomplish his desire.
The instant the monkey observes the flash of the fire of the rifle, it drops from the tree. Will the bullet hit the monkey? Find the radius of curvature of its trajectory in 3 s after the motion has begun. A and B are points on opposite banks of a river of breadth a and AB is at right angles to the flow of the river Fig.
A boat leaves B and is rowed with constant velocity with the bow always directed toward A. If the velocity of the river is equal to this velocity, find the path of the boat Fig. The wheel, which is initially at rest, has a tangential force applied at right angles to its radius of magnitude 50 N as shown in Fig.
The wheel has a moment of inertia equal to 20 kg m 2. Find the minimum value of F Fig. Centre of Mass1. Locate the centre of mass from the diameter of the semicircle. Find the centre of mass. Find the centre of mass of the earth-moon system. Locate the centre of mass of the molecule relative to the carbon atom. Locate the centre of mass of the NH 3 molecule relative to the N atom. A boy of mass 50 kg walks from the bow to the stern.
Find the distance through which the boat moves. If the rod is to move with pure translation, at what fractional length from the loaded end should it be struck? One of the pigeons is shot dead by a hunter and the other four continue to fly with the same speed.
Find the centre of mass speed of the rest of the pigeons which continue to fly with the same speed after the dead pigeon has hit the ground. Locate the centre of mass from the same end. Locate the centre of mass from the fixed point. The centre of mass will lie along the y-axis for reasons of symmetry Fig. Locate the centre of mass from O, the centre of the base. Find the frequency of a small amplitude oscillation of the particle about the equilibrium position.
A tension parallel to the plane is applied by a thread attached to the upper surface. Show that the cube will slide or topple according to the coefficient of friction is less or greater than 0. Therefore in 3 s the distance covered will be 6A. Let the car A overtake B in time t after travelling a distance s. Thus the boy must head toward D on the round, which is The observer is inside the elevator. Take the downward direction as positive. Then from the construction of Fig. The acceleration due to gravity being in the opposite direction is taken negative.
The second solution being negative is ignored. Thus the packet takes 5. Here for simplicity we assume it to be constant.
This limiting velocity is called the terminal velocity. We can obtain an expression for the distance x traversed in time t. First, we identify the constant c in 2. The velocity v in terms of x can be obtained by eliminating t between 5 and 9. Therefore, the bullet would hit the monkey independent of the bullet's initial velocity. After the explosion, one fragment starts falling vertically and so does not carry any momentum initially. The second part of mass 1 2 m proceeds horizontally from the highest point with initial momentum p in order to conserve momentum.
From symmetry the CM must lie on the z-axis, Fig. Let the centre of the original disc be at O, Fig. The hole touches the circumference of the disc at A, the centre of the hole being at C. Taking the origin at the centre of mass L has its centre of mass at C. Let the mass of the wire be M. For stable equilibrium position of the particle it should be a minimum.
Hence it is a minimum corresponding to a stable equilibrium. Take torques about the left-hand side of the edge. Elastic, inelastic and partially elastic collisions in both one dimension and two dimensions are treated. Problems on variable mass cover rocket motion, falling of rain drops, etc. Basic Concepts and Formulae Internal and External ForcesForces acting upon a system due to external agencies are called external forces.
As an example a body placed on a surface is acted by earth's gravitation which is an external force. Forces that act between pairs of particles which constitute the body or a system are all internal to the system and are called internal forces.
The size of a system is entirely arbitrary and is defined by the convenience of the situation. If a system is made sufficiently extensive then all forces become internal forces. By Newton's third law of motion internal forces between pairs of particles get cancelled.
Hence net internal force is zero. Internal forces cannot cause motion. Frames of ReferenceA frame of reference coordinate system is necessary in order to measure the motion of particles.
A reference frame is called an inertial frame if Newton's laws are found to be valid in that frame. It is found that inertial frames move with constant velocity with respect to one another. Conservation Laws i If the total force F is zero, then linear momentum p is conserved.
Conservative ForceIf the force field is such that the work done around a closed orbit is zero, i. A system cannot be conservative if a dissipative force like friction is present. Since the quantity Fds due to friction will always be negative and the integrand cannot vanish, by Stokes theorem the condition for conservative forces given by 2.
The centre of mass moves as if it were a single particle of mass equal to the total mass of the system, acted upon by the total external force and independent of the nature of the internal forces. Motion of a Body of a Variable MassIt is well known that in relativistic mechanics the mass of a particle increases with increasing velocity. However, in Newtonian mechanics too one can give meaning to variable mass as in the following example.
Consider an open wagon moving on rails on a horizontal plane under steady heavy shower. As rain is collected the mass of the wagon increases at constant rate. Other examples are rocket, motion of jet propelled vehicles, an engine taking water on the run. Ballistic pendulum is a device for measuring the velocity of a bullet. The pendulum consists of a large wooden block of mass M which is supported vertically by two cords. A bullet of mass m hits the block horizontally with velocity v and is lodged within it.
As a result of collision the block is raised through maximum height h see prob. What fraction of the initial kinetic energy is transformed into potential energy? What happens to the remaining energy? Justify your answer. Two blocks of mass M 1 and M 2 are attached by a string passing over a pulley of radius r and moment of inertia I 1 as in Fig. Another mass m is placed on the incline of the wedge. The mass m is released from rest on mass M, which is also initially at rest.
Find the accelerations of M and m Fig. Find the acceleration of the centre of mass of the system. Assume that there is no slipping of the string over the pulley and that the coefficient of kinetic friction between the two blocks and between the lower one and the floor is identical. If a horizontal force F is applied to m 1 , calculate the acceleration of m 1 Fig. Work, Power, Energy 2. Determine the total work done on the particle.
A smooth object slides down the ramp and comes down through a height h, Fig. It hits a spring of spring constant k attached inside an opening of a block resting on a frictionless horizontal surface. Find the compression of the spring noting that the block will slide due to the impact Fig. It makes a glancing collision with a second particle of equal mass that is stationary. In what direction do you expect the neutrino to be emitted and what would be its momentum? Assuming that the collision is elastic a calculate the fraction of neutron's kinetic energy transferred to the carbon nucleus and b calculate the velocities of the neutron and the carbon nucleus after the collision.
Show that half of the original kinetic energy is lost. The bullet is arrested within the block which moves 2 m. If the coefficient of kinetic friction between the block and surface of the table is 0. After the collision the particles have equal and opposite velocities. It consists of a large wooden block of mass M which is supported by two vertical cords. When the bullet is fired at the block, it is dislodged and the block is set in motion reaching maximum height h.
If the coefficient of restitution is e, calculate the total time before the ball comes to rest. It reaches the point B. Calculate the magnitude of change in momentum at A and B. At the highest point in its path, it explodes into two pieces of equal masses.
One of the pieces retraces its path towards the cannon. Find the speed of the other fragment immediately after the explosion. The gunman holding the machine gun in his hands can exert an average force of N against the gun.
Find the maximum number of bullets that can be fired per minute. Particles fall from a height of 1. If each particle has a mass of 0. The coefficient of restitution is e. Hence show that the distance travelled by the boat, until the car falls off, is independent of the acceleration of the car.
Variable Mass2. Obtain an expression for b the burn-out velocity; c the time the rocket takes to attain the burn-out velocity ignoring g; and d the mass of the rocket Model Ship Building Practicum 400 as a function of rocket velocity. Find a the rocket thrust, b net acceleration at the beginning, c time to reach the burn-out velocity, d the burn-out velocity. Obtain the equation of motion and discuss its solution.
It therefore pays to pull rather than push at an angle with the horizontal. The difference arises due to the smaller value of the reaction in pulling than in pushing. This fact is exploited in handling a manual road roller or mopping a floor, which is pulled rather than pushed.
Now, these two torques act in opposite directions. As the mass m goes down the wedge the wedge itself would start moving towards left, Fig. Since the external force in the horizontal direction is zero, the component of momentum along the x-direction must be conserved:Fig. Assuming that the string is taut, the acceleration of the two masses must be numerically equal, i.
Let the tension in the string be T. The forces acting on m 2 are tension T 2 due to the string, gravity, frictional force f 2 due to the movement of m 1 and the normal force which m 1 exerts on it to prevent if from moving vertically. The forces on m 1 due to m 2 are equal and opposite to those of m 1 on m 2.
By Newton's third law the tensions T 1 and T 2 in the thread are not equal as the pulley has mass. From the triangle ABC, Fig. Both the objects cannot be scattered in the backward direction.
In that case the x-component of momentum cannot be conserved. If the compression of the spring is x then the spring energy would be 1 2 kx 2.
The negative sign shows that the ball 1 moves toward left after the collision and hits ball 3. Therefore ball 1 will not undergo the third collision with ball 2. Thus in all there will be only two collisions. After the collision both the bodies will be moving in the direction of incidence, the heavier one with velocity v H and the lighter one with velocity v L.
Resolve the momentum along the x-axis and y-axis, Fig. The collision is said to be inelastic. Therefore the scale reading will increase due to the weight of the particles that get accumulated in the pan. After the collision let the final velocities be v 1 and v 2 , respectively, for m 1 and m 2. As t increases, the second term becomes vanishingly small and the first term alone dominates.
Thus y length of the rope hanging down increases exponentially with time. This then is the case of non-uniform acceleration. The pressure on the table consists of two parts: a The weight of the coil on the table producing the pressure and b the destruction of momentum producing the pressure.
Let a length x be coiled up on the table. This problem is solved by equating the centripetal force to the frictional force. Find the tension in the string. The problem is solved by equating the centripetal force to the tension in the string. If it is swung around with a constant frequency f , find the new length L. Solution: A conical pendulum is a simple pendulum which is allowed to execute rotations about the vertical axis.
Assume that a is half of the distance between the wheels and h is the height of the centre of gravity CG of the carriage above the ground. This is countered by an opposite torque caused by the weight of the carriage acting vertically down through the centre of gravity. Solution: At the top the weight acts down while the centrifugal force acts up. If the bob is released from rest it passes through the equilibrium position with velocity v. Find v. If it is gently pushed, it will slide down along the arc of a great circle and leave the surface at B, at depth h below A, Fig.
Determine the position where the particle leaves the sphere. Here we balance the radial component of g at B with the centripetal force. Find the minimum speed at the top so that he may successfully complete the circular ride.
Let a particle start at a height h on the slide and acquire a velocity v at the bottom of the loop. It will oscillate in the lower semicircle about the point D. Problems Motion in a Horizontal Plane3. Determine the magnitude of the velocity when the particle is 3 m from the origin. What time is needed after the motion begins for the normal acceleration of the point to be equal to the tangential acceleration?
Determine the radius of the wheel. From a point on the rim hangs a simple pendulum. If the radius of the wheel is R cm and the length of the pendulum is 1 cm, obtain an expression for the number of rotations of the wheel per second. What is the new length of the spring and the tension in the spring? It is rotated about an axis passing through its centre and perpendicular to the face and a coin is placed on the inside surface of the drum.
The ring rotates with constant speed in a horizontal circle of radius r. The object has a weight of 50 kg wt. What reading is registered on the spring balance? Find the maximum safe speed at which it could travel round the unbanked curve of radius m. The pendulum is put in the horizontal position and released from rest. Motion in a Vertical Plane 3. If the coefficient of friction is 0. What should be the minimum strength of the string in order that it may not break upon passing through the lowest point?
When it passes through the lowest point, the string experiences a tension equal to double the weight of the bob. Loop-the-Loop 3. At what height above the centre of the vertical circle will the bob leave the path? What is the minimum height of the incline? If the particle starts from a point that is level with the highest point on the circular track then find the point where the particle leaves the circular groove above the lowest point.
When m is at the lowest position, its speed is 0. The particle will move up the track to some point p at which it will lose contact with the track and travel along a path shown by the dotted line Fig. Solutions Motion in a Horizontal Plane3. The last relation shows that by virtue of minus sign a is oppositely directed to r , i.
From the geometry of Fig. As the coin tends to slip down under gravity a frictional force would act vertically up. Balancing the x-and z-components of forces Fig. Figure 3. The weight of the carriage acting vertically down through the centre of gravity produces a clockwise torque.
The condition for the maximum speed v max is given by equating these two torques: 3. However, this results in a lot of wear and tear of tyres. Further, the frictional force may not be large enough to cause a sharp turn on a smooth road. If the road is constructed so that it is tilted from the horizontal, the road is said to be banked.
The necessary centripetal force is provided by the horizontal component of the normal reaction N and the horizontal component of frictional force. Three external forces act on the vehicle, and they are not balanced, the weight W , the normal reaction N , and the frictional force. Let it slide down from rest along the arc of the great circle and leave the surface at B, at depth h below A, Fig. At the lowest point B both the centrifugal force and the weight act vertically down and both add up to give the tension T B.
As it passes through C let its speed be v. Measure potential energy with respect to A, the equilibrium position. At the point B, at height L the mechanical energy is entirely potential energy as the bob is at rest. As the vertical height is L, the potential energy will be mgL. When the bob is released, at the point A, the energy is entirely kinetic, potential energy being zero, and is equal to 1 2 mv 2 A.
Drop a perpendicular PE on the horizontal CD. When the bob leaves the point P, the normal reaction must vanish. The weight acts vertically down. Initially the bob of the pendulum is positioned at B at height h above the equilibrium position C.
It is directed at right angles to the axis of rotation, similar to the centrifugal force. However, the direction of the centrifugal force remains unchanged.
The cyclonic motion is found to be mostly in the counterclockwise direction in the northern hemisphere and clockwise direction in the southern hemisphere. The effect of Coriolis force on the motion of the pendulum is to produce a precession or rotation of the plane of oscillation with time.
The plane of oscillation rotates clockwise in the northern hemisphere and counterclockwise in the southern hemisphere. If the spool is let go, find the acceleration and the tension of the string. In which order would these bodies reach the bottom of the incline? Calculate the mean angular velocity of the wheel averaged over the total deceleration time. Find the angle which the rod makes with the vertical.
A uniform rod of length l and mass M rests on a frictionless horizontal surface. The rod pivots about a fixed frictionless axis at one end. The rod is initially at rest. A bullet of mass m travelling parallel to the horizontal surface and perpendicular to the rod with speed v strikes the rod at its centre and becomes embedded in it. Using the result above, show that the angular momentum of the rod after the collision is given by 4.
Suddenly a point on its circumference is fixed. Initially it has an angular velocity and the motion slows down only because of air resistance which is k dx times the square of the velocity on each element of the rod of length dx. If the cylinder is fixed and the sphere does not slide, find T , the time period of oscillations in terms of a, b and g, the acceleration due to gravity.
The disc then encounters a smooth drop of height h, after which it continues to move with velocity v. At all times the disc remains in a vertical plane Fig. How far from its initial position will it land? Neglecting the curvature of the earth, find the magnitude and direction of the Coriolis force. Calculate the displacement from the vertical in 10 s. Solutions Moment of Inertia4. The moment of inertia dI of the disc about the z-axis is given by Fig.
From Fig. Rotational Motion4. At the bottom the potential energy is assumed to be zero. Further the particle velocities v and r are perpendicular. When it falls on the ground the potential energy is converted into kinetic energy rotational.
At the maximum height the kinetic energy is transformed into potential energy. Therefore the body can be either a disc or a solid cylinder. Therefore the order in which the bodies reach is solid sphere, solid cylinder, hollow sphere and hollow cylinder. The physical reason is that the larger the value of k the greater will be I , and larger fraction of kinetic energy will go into rotational motion. Consequently less energy will be available for the translational motion and greater will be the travelling time.
Actually in the transition both may be present. The forces acting at A have no torque at A, so that the angular momentum is conserved. The only forces acting in a horizontal plane are the reactions at P which are equal and opposite.
Consequently G will not move and the angular momentum about G which was zero initially will remain zero throughout the motion due to its conservation. With the choice of a right-handed system, the i -axis is in the southward direction and the j -axis in the eastward direction, Fig.
Assume g the acceleration due to gravity to be constant. The zero potential is chosen conventionally at infinity. Kepler's Laws i All planets move in an elliptic path, with the sun at one focus.
This is a consequence of inverse square law of gravitation and the constancy of total energy and angular momentum. This is a consequence of the constancy of angular momentum. This is a consequence of the inverse square law of gravitation for circular orbits.
Central force is a conservative force which acts along a line connecting the centres of particles. For the satellites the corresponding terms are apogee and perigee. At both perigee perihelion and apogee aphelion the velocity of the orbiting body is perpendicular to the radius vector and they constitute the turning points.
Let f represent force per unit mass. Problems Field and Potential 5. It may slightly deviate through a small angle. The sun is about 9. Calculate the gravitational intensity at the centre O. This is estimated by the differential g which is the difference of the acceleration at B and that at C due to the moon Fig.
Calculate the work done in overcoming gravitational force due to the hemisphere. Figure 5. A particle of mass m is released from a distance R in front of the opening. Calculate the speed with which the particle will hit the point C on the shell, opposite to the opening. Calculate the minimum value of v 0 such that the asteroid does not hit the planet.
Find the eccentricity of the orbit. Each component of a binary star has period of revolution about their centre of mass, equal to Further, the orbit is nearly circular. Calculate a the separation of the two components and b the mass of each component. What is the angular momentum per unit mass of the comet about the sun? The closest distance from the sun that the comet reaches is 0.
What is the speed of the comet at this point? Is the comet's orbit bound or unbound? When it approaches the nearer apse turning point the centre of force is transferred to the other focus. Prove that 5. Show that the new orbit will be a parabola or hyperbola accordingly as the apse is the farther or nearer one. At the perigee nearest point its speed is v and its distance from the centre of the earth is r.
What is its speed at the apogee farthest point? Find the equation of the orbit distinguishing three cases which may arise. Solutions Field and Potential5. Resolve these forces in the horizontal and vertical direction. The horizontal components being in opposite direction get cancelled. The vertical components get added up.
In the absence of rotation the gravitational force mg acts radially towards the centre O and is represented by PO. Drop CD perpendicular on the EW-axis. Then the resultant force mg is given by PD both in magnitude and direction. It is required to find the potential V r at the point P, at distance r from the centre.
The contribution to V r comes from two regions, one V 1 from mass lying within the sphere of radius r and the other V 2 from the region outside it. The field point P is at a distance R from the infinite line. The x-component of gravitational field at P due to this line element will get cancelled by a symmetric line element on the other side.
However, the y-component will add up. The work done to move a particle of mass m to infinity will be 3 4 G Mm R. The gravitational field at P will be effective only from matter within the sphere of radius r. Assume that this mass is concentrated at the centre. P is a point on the z-axis at distance z from the origin. Thus, within the shell its velocity remains unaltered. At the turning point the velocity v of the asteroid will be perpendicular to the radial vector.
At both these points the velocity is perpendicular to the radius vector. At the apogee farthest point , the velocity of the satellite is perpendicular to the radius vector. Therefore the orbit is bound. Let the new semi-major axis be a 1. Case 1: Apse is fartherIt is sufficient to show that the total energy is zero.
Second, it must fly at the right altitude so that its time period is equal to that of the diurnal rotation of the earth. Thus the force is proportional to the inverse fourth power of distance. Chapter 6Oscillations Abstract Chapter 6 deals with simple harmonic motion and its application to various problems, physical pendulums, coupled systems of masses and springs, the normal coordinates and damped vibrations.
The negative sign in 6. It is also independent of the amplitude for small amplitudes. Seconds pendulum is a simple pendulum whose time period is 2 s. Time period of the stationary pendulum is T and that of moving pendulum T.
In the equilibrium position the centre of mass C lies vertically below the pivot P. When displaced through a small angle about the vertical wire and released the oscillator would execute oscillations in the horizontal plane. The solutions of 6. A deeper insight is obtained from the energies expressed in normal coordinates as opposed to the old coordinates. Each normal coordinate corresponds to an independent mode of vibration of the system, with its own characteristic frequency and the general vibratory motion may be regarded as the superposition of some or all of the independent normal vibrations.
The presence of the dissipative forces results in the loss of energy in heat motion leading to a gradual decrease of amplitude. Distinct real roots. Both the exponential terms in 6.
The motion is not oscillatory. The general solution is of the form The exponentials in the square bracket may be expanded to terms linear in Rt. It is a transition case and the motion is just aperiodic or non-oscillatory. Calculate the amplitude of motion and mass of the particle. Find a the amplitude; b the time period of motion. Find the velocity of the bob and the tension in the supporting thread when velocity of the bob is maximum. Ignore the viscous forces. If the mass is increased by 2 kg, the period increases by 1 s.
Assuming that Hooke's law is obeyed, find the initial mass M. Find the amplitude and the period of oscillation of the particle. Determine a the spring constant; b maximum force exerted on the spring. Determine the path of the particle. The weight is pulled down a distance of 10 cm and released. Find a the spring constant; b the amplitude; c the frequency of oscillations. The collision may be considered to be completely inelastic in that the mass sticks to the pan and the pan begins to oscillate.
Find the amplitude of the pan's oscillations. Find the time period of oscillations. If they are set in motion simultaneously, find the time taken for one to gain a complete oscillation on the other. How much time will the pendulum lose in 1 day? Assume earth's radius to be km.
If the liquid on one side is slightly depressed by blowing gently down, the levels of the liquid will oscillate about the equilibrium position before finally coming to rest. The gas occupies a length l in the equilibrium position and is at pressure P. Calculate the mass of the spring.
Show that a when two springs are stretched by the same amount, more work will be done on the stiffer spring. Determine the time period. Physical Pendulums 6. Such a system is called a physical pendulum. What would be the length l of a simple pendulum that has the same period as the swinging rod? If slightly tilted through a small angle and released, find the angular frequency of oscillations. It can oscillate in its plane with time period T 1 or it can oscillate back and forth in a direction perpendicular to the plane of the ring with time period T 2.
Assuming that the mass of the thread and the spring is negligible and that the thread does not slide over the frictionless pulley, calculate the angular frequency of small oscillations. Assuming that the cylinder rolls without sliding, find the time period.
Coupled Systems of Masses and Springs6. Calculate the effective spring constant. Assuming that the cylinder rolls without slipping, calculate the natural frequency of oscillation of the system. Damped Vibrations6. Determine the logarithmic decrement. Find a amplitude; b phase lag; c Q factor; d power dissipation. If its time constant is 2 s, determine the Q factor for the bell. By what factor is its amplitude decreased in each cycle? It is then slightly pulled down and released.
Assuming that the logarithmic decrement is equal to 3. Find the Q factor. The acceleration g points opposite to the displacement x. Here G is the centre of mass CM of the physical pendulum. The twisted wire will exert a restoring torque on the disc causing the reference line to move to its original position.
For small twists the restoring torque will be proportional to the angular displacement in accordance with Hooke's law. Then the spring at C is compressed by x while the spring at P is elongated by 2x. We use the energy method. The first term on the right side gives the torque of the force mg, which is force times the perpendicular distance from the vertical through P.
The second equation of motion can be similarly written. These new coordinates X 1 and X 2 , called normal coordinates, vary harmonically with but a single frequency. No energy transfer occurs from one normal coordinate to another.
They are completely independent. Thus when equations of motion are expressed in normal coordinates, the equations are linear with constant coefficients and each contains only one dependent variable. We now calculate the energy in normal coordinates. The potential energy arises due to the energy stored in the spring and due to the position of the body. The presence of the crossproduct term means coupling between the components of the vibrating system.
However, in normal coordinates the cross-product terms are avoided. The potential energy V is now expressed as a sum of squares of normal coordinates multiplied by constant coefficients and kinetic energy. T is expressed in the form of a sum of squares of the time derivatives of the normal coordination.
We can now describe the mode of oscillation associated with a given normal coordinate. The mode X 1 is shown in Fig. Here the spring plays no role because it remains unstretched throughout the motion. Here the pendulums are out of phase. The X 2 mode is also illustrated in Fig. C and D can be determined from initial conditions.
Basic Concepts and FormulaeNewtonian mechanics deals with force which is a vector quantity and therefore difficult to handle. On the other hand, Lagrangian mechanics deals with kinetic and potential energies which are scalar quantities while Hamilton's equations involve generalized momenta, both are easy to handle. While Lagrangian mechanics contains n differential equations corresponding to n generalized coordinates, Hamiltonian mechanics contains 2n equation, that is, double the number.
However, the equations for Hamiltonian mechanics are linear. Eqn 2 is applicable to all the conservative systems. When n independent coordinates are required to specify the positions of the masses of a system, the system is of n degrees of freedom.
Determine the equations of motion. Write down Hamiltonian's equation and find the general solution. First, assume that the bowl does not move. Hence, derive the equation of motion for the particle. Define the generalized momentum associated with q and the corresponding Hamiltonian, H q, p.
Derive Hamilton's equations from Lagrange's equations of the system. For the remainder of the question, consider the system whose Lagrangian, L q,q. Find the corresponding Hamiltonian and write down Hamilton's equations. What characteristic feature should the Lagrangian function have for a generalized momentum to be a constant of motion? A particle P can slide on a frictionless horizontal table with a small opening at O.
It is attached, by a string of length l passing through the opening, to a particle Q hanging vertically under the table see Fig. The two particles have equal mass, m. The particle is connected to the origin by a spring, as shown in the diagram, and is subject to gravity. The potential energy in the spring is 1 2 kr 2 where r is the distance of the point mass from the origin Fig. You may either use Lagrange's equation or proceed directly from the potential energy.
In particular 11 signifies the constancy of areal velocity or equivalently angular momentum Kepler's second law of planetary motion. The solution of 10 leads to the first law which asserts that the path of a planet describes an ellipse.
This example shows the simplicity and power of Lagrangian method which involves energy, a scalar quantity, rather than force, a vector quantity in Newton's mechanics. Then Fig. The double machine is an Atwood machine in which one of the weights is replaced by a second Atwood machine, Fig.
The system now has two degrees of freedom, and its instantaneous configuration is specified by two coordinates x and x. The coordinate on the horizontal axis is described by x for the inclined plane and x for the block of mass m on the incline.
The origin of the coordinate system is fixed on the smooth table, Fig. The x-and y-components of the velocity of the block are given byFig. It is conserved because torque is not produced either by gravity or the tension of the cord about the z-axis.
Thus conservation of angular momentum is reflected in 5. Two interesting cases arise. The kinetic energy of the system comes from the motion of the blocks and potential energy from the coupling spring:Fig. We are then left with only two canonical equations to be solved.
Then H varies with time for two reasons: first, because of its explicit dependence on t, second because the variable q and p are themselves functions of time. The net change is induced by the fact that the variation of q and p with time is zero. Now in a conservative system, neither T nor V contains any explicit dependence on time. The first one corresponds to symmetric mode of oscillation and the second one to asymmetric one. Similarly 22 is a linear equation in q 1 with constant coefficients.
Since the coefficients on the right sides are positive quantities, we note that both 21 and 22 are differential equations of simple harmonic motion having the frequencies given in It is the characteristic of normal coordinates that when the equa-tions of motion are expressed in terms of normal coordinates they are linear with constant coefficients, and each contains but one dependent variable.
Another feature of normal coordinates is that both kinetic energy and potential energy will have quadratic terms and the cross-products will be absent. This corresponds to a symmetric mode as both the amplitudes have the same sign. This corresponds to asymmetric mode. These two modes of oscillation are depicted in Fig. The two normal modes are sketched in Fig. This mode of oscillation is depicted in Fig. This problem has a bearing on the vibrations of linear molecules such as CO 2.
The middle particle represents the C atom and the particles on either side represent O atoms. Here too there will be three modes of oscillations. In Fig. Hence dipole radiation is not emitted for this mode. Both kinetic energy and potential energy arise from the particle alone. Taking the origin at O, the centre of the bowl, Fig.
There is only one degree of freedom:Fig. The total kinetic energy then comes from the motion of both the particle and the bowl. The n equation of type 3 are employed for this purpose.
Each provides one of the p's in terms of theq s. These are 2n is number. For a system with n degrees of freedom the n Lagrangian equations 2 of the second order are replaced by 2n Hamiltonian equations of the first order. We note from the second equation of 11 that if any coordinate q l is not contained explicitly in the Hamiltonian function H , the conjugate momentum p l is a constant of motion.
Such coordinates are called ignorable coordinates. If the Lagrangian of a dynamical system does not contain a certain coordinate, say q s , explicitly then p s is a constant of motion. The potential energy arises from the particle Q alone. Therefore P describes a circle of constant radius a. This aspect of oscillations has a bearing on the so-called betatron oscillations of ions in circular machines which accelerate charged particles to high energies.
If the amplitudes of the betatron oscillations are large then they may hit the wall of the doughnut and be lost, resulting in the loss of intensity of the accelerated particles. From the geometry of the diagram Fig. The superposition principle states that when two or more waves traverse the same region independently, the displacement of any particle at a given time is given by the vector addition of the displacement due to the individual waves.
Interference of waves: Interference is the physical effect caused by the superposition of two or more wave trains crossing the same region simultaneously. The wave trains must have a constant phase difference. Vibrating strings: Stationary waves are formed by the superposition of two similar progressive waves travelling in the opposite direction over a taut string clamped by rigid supports.
The general solution of 8. The amplitude has a minimum value of zero nodes. Ends of the strings are always nodes. Neighbouring nodes and antinodes are spaced onequarter wavelength apart. In all these cases the material of restricted dimension is considered. Waves in LiquidsThe wave motion through liquids is influenced by the gravity and the characteristics of the medium such as the depth and surface tension. Canal WavesIf the wavelength is large compared with the wave amplitude, surface tension effect is small.
The controlling factors are then basically gravity g and the boundary conditions. Furthermore, if the surface is sufficiently extensive so that the wall effects are negligible then the depth h alone is the main boundary condition. Doppler effect is the apparent change in frequency of a wave motion when there is relative motion between the source and the observer.
The wave front assumes the shape of a cone with the moving body at the apex. An example of shock waves is the wave resulting from a bow boat speeding on water, a second example is a jet-plane or missile moving at the supersonic speed, a third example is the emission of Cerenkov radiation when a charged particle moves through a transparent medium with a speed exceeding that of the phase velocity of light in that medium. Echo is defined as direct reflection of short duration sound from the surface of a large area.
Beats: When two wave trains of slightly different frequencies travel through the same region, a regular swelling and fading of the sound is heard, a phenomenon called beats. Problems Vibrating Strings 8. Obtain an expression for the displacement y at any point x and time t as a series expansion assuming that initially the velocity is zero.
An incorporated city is authorized to contract with a private institution of higher education for the use and employment of its commissioned officers in any manner agreed to, provided that there is no expense incurred by the city. For purposes of this section, a private institution of higher education is a private or independent institution of higher education as defined by Section The agreement must be reviewed at least annually by the institution and the municipality and may be modified at that time by a written agreement signed by each party.
The agreement may be terminated at any time by a party to the agreement on the provision of reasonable notice to the other party to the agreement. The municipal law enforcement agency has exclusive authority to supervise any campus peace officer operating under the agreement to assist the peace officers of the municipality. A municipal peace officer operating under the agreement to assist the campus peace officers remains under the supervision of the municipal law enforcement agency.
Acts , 81st Leg. June 19, If a campus peace officer elects to appeal the institution's action to an independent third party hearing examiner under this section, the officer or institution may appeal the examiner's decision to a district court only as provided by Subsection j.
If the parties do not agree on the selection of a hearing examiner before the 10th day after the date the appeal is filed, the parties immediately shall request a list of seven qualified neutral arbitrators from the American Arbitration Association or the Federal Mediation and Conciliation Service, or their successors in function. The officer and the agency head or their designees may agree on one of the seven neutral arbitrators on the list.
If the parties do not agree before the fifth business day after the date the parties receive the list, the parties or their designees shall alternate striking a name from the list, and the single name remaining after all other names have been struck is selected as the hearing examiner.
The parties or their designees shall agree on a date for the hearing. If the hearing examiner cannot begin the hearing before the 45th day after the date of selection, the campus peace officer may, within 48 hours after learning of that fact, call for the selection of a new hearing examiner using the procedure prescribed by Subsection d.
The hearing examiner may:. Unless otherwise agreed by the parties, in an expedited procedure the hearing examiner shall issue a decision on the appeal not later than the 10th day after the date the hearing is completed.
The hearing examiner's inability to meet the time requirements imposed by this section does not affect the hearing examiner's jurisdiction, the validity of the disciplinary action or promotional bypass, or the hearing examiner's final decision. The costs of a witness shall be paid by the party who calls the witness.
An appeal must be brought in the district court having jurisdiction in the municipality in which the institution is located. Added by Acts , 65th Leg. The employing medical corporation or parent corporation shall pay to the Texas Commission on Law Enforcement on behalf of an employee any fees that are necessary to obtain a required license. Added by Acts , 67th Leg. June 11, March 31, ; Acts , 77th Leg. The institution of higher education may deny employment to an applicant for a security-sensitive position who fails to provide a complete set of fingerprints upon request.
Security-sensitive positions shall be restricted to employees who handle currency, have access to a computer terminal, have access to a master key, or who work in an area of the institution which has been designated as a security-sensitive area.
A security-sensitive position shall be so identified in the job description and advertisement for the position. Added by Acts , 68th Leg.
June 11, ; Acts , 71st Leg. June 15, ; Acts , 73rd Leg. The plan must address mitigation, preparedness, response, and recovery. The plan must provide for:. To the extent possible, an institution shall follow safety and security audit procedures developed in consultation with the division of emergency management of the office of the governor. In this subsection, "personal information" includes an e-mail address or telephone number maintained in order to notify an individual of an emergency.
Added by Acts , 81st Leg. The emergency alert system must use e-mail or telephone notifications in addition to any other alert method the institution considers appropriate to provide timely notification of emergencies affecting the institution or its students and staff.
An election under this subsection may be submitted electronically or in writing, as chosen by the institution, and must be renewed at the start of each academic year. Added by Acts , 83rd Leg. June 14, The governing board may, but shall not be required to, reimburse the amount paid by the applicant to participate in the training program under that section.
The written regulations must also require that a handgun carried by or within access of a school marshal may be loaded only with frangible duty ammunition approved for that purpose by the Texas Commission on Law Enforcement. The notice may not disclose information that is confidential under Subsection h. Added by Acts , 84th Leg. Acts , 85th Leg. For purposes of this subchapter a period of disruption is any period in which it reasonably appears that there is a threat of destruction to institutional property, injury to human life on the campus or facility, or a threat of willful disruption of the orderly operation of the campus or facility.
When the chief administrative officer of a campus or other facility of a state-supported institution of higher education, or an officer or employee of the institution designated by him to maintain order on the campus or facility, decides to withdraw consent for any person to remain on the campus or facility, he shall notify that person in writing that consent to remain is withdrawn.
The written notice must contain all of the following:. Whenever consent is withdrawn by any authorized officer or employee other than the chief administrative officer, the officer or employee shall submit a written report to the chief Model Ship Building Practicum Gas administrative officer within 24 hours, unless the authorized officer or employee has reinstated consent for the person to remain on the campus.
The report must contain all of the following:. The written request must state the address to which notice of hearing is to be sent. The chief administrative officer shall grant a hearing not later than three days from the date of receipt of the request and shall immediately mail a written notice of the time, place, and date of the hearing to the person.
In no instance shall the person issuing the withdrawal notice or causing it to be issued serve on any committee where the validity of his order of withdrawal is in question. The chief administrative officer shall reinstate consent whenever he has reason to believe that the presence of the person from whom consent was withdrawn will not constitute a substantial and material threat to the orderly operation of the campus or facility. This subchapter does not affect the power of the duly constituted authorities of a state-supported institution of higher education to suspend, dismiss, or expel any student or employee at the university or college.
No person may refuse or fail to leave a building under the control and management of a public agency, including a state-supported institution of higher education, during those hours of the day or night when the building is regularly closed to the public, upon being requested to do so by a guard, watchman, or other employee of a public agency, including a state-supported institution of higher education, controlling and managing the building or property, if the surrounding circumstances are such as to indicate to a reasonable person that the individual or individuals have no apparent lawful business to pursue.
A person from whom consent to remain on the campus of a state-supported institution of higher education has been withdrawn in accordance with Section A person who violates Section Section f. A in the employment context, unreasonably interferes with a person's work performance or creates an intimidating, hostile, or offensive work environment; or.
B in the education context, is sufficiently severe, persistent, or pervasive that the conduct interferes with a student's ability to participate in or benefit from educational programs or activities at a postsecondary educational institution. Added by Acts , 86th Leg. This subsection does not affect the employee's duty to report an incident under any other law.
The report:. A the number of reports received under Section B the number of investigations conducted as a result of those reports;. C the disposition, if any, of any disciplinary processes arising from those reports;. D the number of those reports for which the institution determined not to initiate a disciplinary process, if any; and. E any disciplinary actions taken under Section A persons employed by or under contract with the postsecondary educational institution to which the report is made who are necessary to conduct an investigation of the report or any related hearings;.
B a law enforcement officer as necessary to conduct a criminal investigation of the report;. C the person or persons alleged to have perpetrated the incident, to the extent required by other law; or. D potential witnesses to the incident as necessary to conduct an investigation of the report. In determining the amount of the penalty, the coordinating board shall consider the nature of the violation and the number of students enrolled at the institution.
The coordinating board shall adopt rules as necessary to implement and enforce this subchapter, including rules that ensure implementation of this subchapter in a manner that complies with federal law regarding confidentiality of student educational information, including the Family Educational Rights and Privacy Act of 20 U. Section g. In adopting those rules, the coordinating board shall use the negotiated rulemaking procedures under Chapter , Government Code, and consult with relevant stakeholders.
Section f 6 A. The policy must:. C the protocol for reporting and responding to reports of sexual harassment, sexual assault, dating violence, and stalking;. D interim measures to protect victims of sexual harassment, sexual assault, dating violence, or stalking during the pendency of the institution's disciplinary process, including protection from retaliation, and any other accommodations available to those victims at the institution; and.
The institution shall establish the format and content of the orientation. The orientation:. The program must:. A e-mailing the information to each student at the beginning of each semester or other academic term; and. B including the information in the orientation required under Subsection c. Added by Acts , 85th Leg. June 12, Transferred, redesignated and amended from Education Code, Section In determining whether to investigate the alleged incident, the institution shall consider:.
A postsecondary educational institution that initiates a disciplinary process concerning an allegation that a student enrolled at the institution violated the institution's code of conduct by committing sexual harassment, sexual assault, dating violence, or stalking shall:. Each peace officer employed by a postsecondary educational institution shall complete training on trauma-informed investigation into allegations of sexual harassment, sexual assault, dating violence, and stalking.
To facilitate effective communication and coordination regarding allegations of sexual harassment, sexual assault, dating violence, and stalking at the institution, a postsecondary educational institution shall enter into a memorandum of understanding with one or more:.
A one or more employees to act as responsible employees for purposes of Title IX of the Education Amendments of 20 U. Section et seq. B one or more employees as persons to whom students enrolled at the institution may speak confidentially concerning sexual harassment, sexual assault, dating violence, and stalking; and.
The institution shall notify each student enrolled at the institution of the student advocates designated under this subsection. A the postsecondary educational institution to which the report described by Subsection a is made as necessary to conduct an investigation of the report;. B a law enforcement officer as necessary to conduct a criminal investigation of the report described by Subsection a ; or.
C a health care provider in an emergency situation, as determined necessary by the institution. The provider must provide aggregate data or other nonidentifying information regarding those incidents to the institution's Title IX coordinator.
In implementing the requirements under this subchapter, a postsecondary educational institution shall, to the greatest extent practicable, ensure equal access for students enrolled at or employees of the institution who are persons with disabilities. The institution shall make reasonable efforts to consult with a disability services office of the institution, advocacy groups for people with disabilities, and other relevant stakeholders to assist the institution with complying with the institution's duties under this section.
Each member must be a chief executive officer of a postsecondary educational institution or a representative designated by that officer. This course shall have a credit value of not less than six semester hours or its equivalent. Except as provided by Subsection c , a college or university receiving state support or state aid from public funds may not grant a baccalaureate degree or a lesser degree or academic certificate to any person unless the person has credit for such a course.
The college or university may determine that a student has satisfied this requirement in whole or in part on the basis of credit granted to the student by the college or university for a substantially equivalent course completed at another accredited college or university or on the basis of the student's successful completion of an advanced standing examination administered on the conditions and under the circumstances common for the college or university's advanced standing examinations.
The college or university may grant as much as three semester hours of credit or its equivalent toward satisfaction of this requirement for substantially equivalent work completed by the student in the program of an approved senior R.
The course must concentrate on important texts, including the United States Constitution and the Declaration of Independence, on the works and contributions of influential authors, political and cultural leaders, and other important figures, and on important events and developments in United States history.
The course must cover important developments in human and civil rights, including the civil rights movement and the history of women's rights. The course must cover the history and development of the State of Texas and its place in United States history and culture.
The course must consist of four semester credit hours, with one semester credit hour in practicum activities intended to provide the student with experience in the three branches of government through participation at the federal, state, or local level.
The course may not be taken for course credit by a student other than a student described by Subsection c.
March 23, ; Acts , 74th Leg. June 16, A student is entitled to submit as much as three semester hours of credit or its equivalent in Texas History in partial satisfaction of this requirement. The college or university may determine that a student has satisfied this requirement in whole or part on the basis of credit granted to the student by the college or university for a substantially equivalent course completed at another accredited college or university, or on the basis of the student's successful completion of an advanced standing examination administered on the conditions and under the circumstances common for the college or university's advanced standing examinations.
The college or university may grant as much as three semester hours of credit or its equivalent toward satisfaction of this requirement for substantially equivalent work completed by a student in the program of an approved senior R. March 23, A student is entitled to count credit received for a course in American Sign Language toward satisfaction of a foreign language requirement of the institution of higher education where it is offered. Amended by Acts , 66th Leg. The governing board of any state-supported institution of higher education may request the United States Department of Defense to establish and maintain courses in military and naval training qualifying men student graduates of the courses for reserve commission awards as a part of its curriculum.
The board may enter into mutually agreeable contracts for that purpose. The work of the students enrolling in the courses may be credited toward degree requirements under regulations prescribed by the board.
A describes the substance of the training completed by the student; and. B verifies the student's successful completion of that training; and. Added by Acts , 79th Leg.
June 18, A completed at least two years of service in the armed forces; or. The Texas Higher Education Coordinating Board shall adopt rules necessary for the administration of this subchapter. Added by Acts , 73rd Leg. May 24, Redesignated from Sec. A driver education course for the purpose of preparing students to obtain a driver's license may be offered by an institution of higher education, as defined by Section Added by Acts , 74th Leg.
Renumbered from Education Code Sec. June 10, This subchapter does not apply to:. B service as a member of a reserve component of the armed forces of the United States. The board shall prescribe a single standard or set of standards for each assessment instrument to effectively measure student readiness as demonstrated by current research. The plan must be designed on an individual basis to provide the best opportunity for each student to attain that readiness.
Each institution shall ensure that at least 75 percent of the institution's students enrolled in developmental coursework other than adult basic education or basic academic skills education are enrolled in developmental coursework described by this subsection. The types of developmental coursework may include:. The institution must make its determination using learning outcomes for developmental education courses developed by the board based on established college and career readiness standards and student performance on one or more appropriate assessments.
An exemption under this subsection is effective for the five-year period following the date a student takes the test and achieves the standard set by the board.
The exemption is effective for the three-year period following the date a student takes the last assessment instrument for purposes of this subchapter and achieves the standard set by the board. This subsection does not apply during any period for which the board designates the questions developed for end-of-course assessment instruments under Section The commissioner of higher education by rule shall establish the period for which an exemption under this subsection is valid.
The exemption is effective for the two-year period following the date the student graduates from high school. The exemption applies only at the institution of higher education that partners with the school district in which the student is enrolled to provide the course, except that the commissioner of higher education by rule may determine the manner in which the exemption may be applied to institutions of higher education other than the partnering institution.
If the student earns a grade below a "C" for the course, the institution shall advise the student of non-course-based options for attaining college readiness, such as tutoring or accelerated learning. The board, in consultation with institutions of higher education, shall develop and provide professional development programs, including instruction in differentiated instruction methods designed to address students' diverse learning needs, to faculty and staff who provide developmental coursework, including basic academic skills education, to students.
B 18 semester credit hours, if the developmental coursework is English for speakers of other languages; and. B 27 semester credit hours, if the developmental coursework is English for speakers of other languages. The board may develop a performance funding formula by which institutions of higher education may receive additional funding for each student who completes the success initiative established under this subchapter and then successfully completes college coursework.
The legislature may appropriate the money required to provide the additional funding under those formulas. Each institution of higher education, other than a medical and dental unit, shall report annually to the board on the success of its students and the effectiveness of its success initiative.
An institution of higher education that administers an assessment instrument to students under this subchapter shall report to each school district from which assessed students graduated high school all available information regarding student scores and performance on the assessment instrument and student demographics.
The board shall evaluate the effectiveness of the success initiative on a statewide basis and with respect to each institution of higher education. Section d et seq. Section g , and any state law relating to the privacy of student information. In this regard each governing board:. In addition to specific responsibilities imposed by this code or other law, each institution of higher education has the general responsibility to serve the public and, within the institution's role and mission, to:.
Not later than January 1, from among the applications received by the student government, the student government shall select five applicants as the student government's recommendations for the position of student regent and send the applications of those applicants to the chancellor of the university system.
From among those applicants, the chancellor shall select two or more applicants as the university system's recommendations for the position of student regent and shall send the applications of those applicants to the governor not later than February 1. The governor may request to review all applications for the position of student regent received by the student governments and may request an applicant to submit additional information to the governor.
On June 1, or as soon thereafter as practicable, the governor shall appoint one of the applicants to serve as the student regent for the system for a one-year term expiring on the next May The governor is not required to appoint an applicant recommended by the chancellor, but may not appoint a student regent who did not submit an application to the student government of a general academic teaching institution or medical and dental unit in the system as described by this subsection.
The person must remain enrolled at the institution throughout the person's term as a student regent. For purposes of this subsection, a person is considered to be enrolled in an institution or unit for a summer term if the person was enrolled in the institution or unit for the preceding semester and:.
The president of the institution in which the student regent is enrolled shall notify the governor if the student regent fails to maintain the qualifications required by this section. A student regent has the same powers and duties as the members of the board of regents of the system, including the right to attend and participate in meetings of the board of regents, except that the student regent:.
May 23, Not later than January 1, from among the applications received by the student government, the student government shall select five applicants as the student government's recommendations for the position of student regent and send the applications of those applicants to the president of the institution.
From among those applicants, the president shall select two or more applicants as the institution's recommendations for the position of student regent and shall send the applications of those applicants to the governor not later than February 1.
The governor may request to review all applications for the position of student regent received by the student government and may request an applicant to submit additional information to the governor. On June 1, or as soon thereafter as practicable, the governor shall appoint one of the applicants to serve as the student regent for the institution for a one-year term expiring on the next May The governor is not required to appoint an applicant recommended by the president, but may not appoint a student regent who did not submit an application to the student government of the institution as described by this subsection.
For purposes of this subsection, a person is considered to be enrolled in an institution for a summer term if the person was enrolled in the institution for the preceding semester and:. A student regent has the same powers and duties as the members of the board of regents of the institution, including the right to attend and participate in meetings of the board of regents, except that the student regent:.
Renumbered from Education Code, Section Each institution of higher education shall develop a statement regarding the role and mission of the institution reflecting the three missions of higher education: teaching, research, and public service. Transferred and redesignated from Education Code, Section It is the intent of the legislature that all public higher education institutions of this state shall manage their institutions and institutional resources to achieve maximum effectiveness and to provide the greatest attainable educational benefit from the expenditure of public funds.
In adopting rules under this subsection, each institution shall recognize that classroom teaching, basic and applied research, and professional development are important elements of faculty academic workloads by giving appropriate weight to each activity when determining the standards for faculty academic workload.
An institution may give the same or different weight to each activity and to other activities recognized by the institution as important elements of faculty academic workloads.
The established rules and regulations of each institution shall be included in the operating budgets of each institution. The report of academic duties and services performed by each member of the faculty shall indicate all appointments held by the faculty member in the employing institution, the salary paid to each appointment, the percent of time of each appointment, and the source of funds from which salary payments were made.
Teaching responsibilities in each workload standard shall be in proportion to the portion of salary paid from funds appropriated for instructional purposes. This report shall include, but not be limited to, appropriate student test scores, a description of developmental courses required, and the student's grade point average.
Appropriate safeguards for student privacy shall be included in the rules for implementation of this subsection. D the level of education achieved by the parents of students; and. Not later than December 1 of each year and in the form prescribed by the coordinating board, each general academic teaching institution Model Ship Building Practicum 5g and medical and dental unit as defined in Section The report must include a demographic breakdown of the class, including a breakdown by race, ethnicity, economic status, and high school class standing.
A report submitted by a general academic teaching institution or medical and dental unit as defined in Section A the Workforce Education Course Manual or its successor adopted by the coordinating board; or. Each institution shall submit all reports required by this subchapter to the coordinating board.
The coordinating board shall furnish such summaries of these reports as the governor's budget office and legislative budget board may request, including an analysis of compliance by each institution of higher education with its adopted rules and regulations as filed with the coordinating board in compliance with Section All such reports shall be public information. Should any institution of higher education fail to comply with its adopted rules and regulations as determined by the coordinating board in Section This subsection does not apply to:.
A Article B Section C Section E Section J Section M Chapter , Insurance Code. The coordinating board shall consult with those entities to identify unnecessary data requests and shall eliminate data requests identified as unnecessary from its rules and policies. In this subsection, "private or independent institution of higher education" has the meaning assigned by Section B in a contractual relationship or otherwise affiliated with an institution of higher education.
A an institution of higher education as defined by Section B a private or independent institution of higher education as defined by Section The term may include full course curricula, course materials, modules, textbooks, media, assessments, software, and any other tools, materials, or techniques, whether digital or otherwise, used to support access to knowledge. The term includes any edition of a textbook or set of textbooks and any item considered supplemental specifically to the textbook, regardless of whether the textbook and supplemental item are sold together or separately.
The term does not include a textbook that is combined with other instructional material if that material in its entirety is:. A required to be offered for sale with or as part of the textbook, according to a third-party contractual agreement; or.
B interrelated with the content of the textbook to such a degree that any separation of the material from the textbook would render the textbook unusable for its intended purpose. June 9, E the International Standard Book Number assigned, if any; and. F whether the textbook is an open educational resource;. A publish the textbook list with the course schedule on the institution's Internet website and with any course schedule the institution provides in hard copy format to the students of the institution; and.
B make that information available to college bookstores and other bookstores that generally serve the students of the institution; and. To the extent practicable, an institution of higher education shall make reasonable efforts to disseminate to its students information regarding:. A textbook publisher that offers a textbook bundle for sale directly to students enrolled at an institution of higher education or, for resale purposes, to a college bookstore or other bookstore that generally serves the students of the institution shall also offer for sale to the students or bookstore, as applicable, each individual item of instructional material as a separate, unbundled item that is separately priced.
The purpose of this subchapter is to establish a private donor research fund to encourage donations from the private sector to support research and development in teacher education and teaching. III, part J, Sec. In addition, the board shall adopt standards and timetables for the projects it assigns and shall periodically review the progress of the projects. Added by Acts , 69th Leg. In this subchapter, "institution of higher education" has the meaning assigned by Section The agreements shall in no way abrogate the powers and duties of the boards with regard to the governance of their respective institutions.
The governing boards of the participating institutions shall appoint an advisory committee composed of three members from each board.
The committee shall study the needs of the community served by the institutions and shall make recommendations to the respective boards concerning the development of coordinated programs and services to meet those needs. The committee shall give particular attention to the continuity of curriculum offerings and to the joint use of faculty and staff, facilities, and library resources. By interagency contract the governing boards of the participating institutions may fill by joint appointment any administrative, faculty, or support position necessary for the operation of the institutions.
In such cases, salaries and benefits shall be prorated and paid from the funds of the respective institutions according to the share of each employee's responsibility to each institution. By interagency contract the governing boards of the participating institutions may assign the management and operation of selected services to one of the institutions in order to achieve cost effectiveness. Such services include, but are not limited to, maintenance of building and grounds, operation of auxiliary enterprises, and operation of a jointly supported library.
Amended by Acts , 78th Leg. The role and scope of the other participating institution of higher education are subject to approval by the coordinating board. In this review, the commissioner shall determine, as a ministerial duty, without regard to the substance of the content thereof, whether the intellectual property policies address as a minimum standard the following matters:. Thereafter, an institution of higher education may file or post on the institution's website on the Internet in a manner available to the public policies amended to overcome any failure to meet the standards.
The commissioner shall within a reasonable time after receiving an amended policy inform the submitting institution whether it meets the standards. The commissioner of higher education shall establish procedures for the monitoring of this policy of the state. The legislature finds that:. Manufacturing has the highest economic multiplier of any industrial sector, contributing to economic growth and personal wealth. High technology manufacturing has the highest economic multiplier among manufacturing sectors;.
Texas, as a primary producer of raw materials, finds itself positioned to benefit tremendously from improvement and development of its manufacturing capabilities, even while the Texas economy suffers the consequences of having depended too heavily on production of raw materials alone; and.
It is the intent of the legislature that Texas accept the challenge of becoming the nation's centerpoint for advanced manufacturing technology development by aggressively pursuing the siting in Texas of the National Center for Manufacturing Sciences, proposed by the National Academy of Sciences and the Manufacturing Science Board, and initiated by the National Machine Tool Industry.
With this centerpiece for advanced research and technology transfer in the area of manufacturing sciences, Texas could become a primary producer of high value-added products, with enormous benefits for the entire economy.
In this subchapter, "fund" means the fund for the National Center for Manufacturing Sciences. April 29, Amended by Acts , 75th Leg. Each public senior college or university in the state shall participate in the Educational Economic Policy Center at the request of the governor. The center shall represent business, finance, public policy, education, and other appropriate disciplines.
The center shall monitor and evaluate the implementation of the accountability system under Chapters 39 and 39A. The office of the governor may receive grants and donations for the purposes of this subchapter.
The center may participate in collaborative studies with foundations or organizations within or outside the state.
Added by Acts , 71st Leg. May 30, Amended by Acts , 76th Leg. The committee shall study the elements of a quality educational system to:. The governor, lieutenant governor, and speaker of the house of representatives shall each appoint two members, only one of whom may be a board member or employee of a public school district, college, or university. Those appointees shall include persons in the private sector who have an interest in improving public education.
In addition, the governor shall appoint three members who serve on the boards of regents representing the universities or systems participating in the center. In this subchapter, "board," "general academic teaching institution," "governing board," "institution of higher education," "public state college," "public technical institute," "private or independent institution of higher education," and Model Ship Building Practicum 903 "university system" have the meanings assigned by Section A a common admission application form for use by a person seeking admission as a freshman student to a general academic teaching institution;.
B an electronic common admission application form for use by a person seeking admission as a freshman student to an institution of higher education that admits freshman-level students, other than a general academic teaching institution; and. C if the board determines that adoption of the form would be cost-effective for nursing schools, an electronic common admission application form for use by a person seeking admission as a student to an undergraduate nursing education program at an institution of higher education; and.
The form used to apply to a general academic teaching institution may be filed in either electronic or printed format. An institution of higher education is not prohibited from requiring an applicant to submit additional information within a reasonable time after the institution has received an application using a form adopted under this section.
A apply electronically to one or more of the general academic teaching institutions within the university system; and. B indicate preferences for admission between those institutions; and. This subchapter does not affect the authority of an institution of higher education to receive a reasonable fee for the filing of an application for admission.
Added by Acts , 75th Leg. A status or lack of status as a party to the agreement; or. A board may, as appropriate, delegate by rule its authority under this subchapter to its designated representative. The institution shall publish in the request for bids, proposals, or qualifications the criteria that will be used to evaluate the offerors. The design criteria package must specify criteria the institution considers necessary to describe the project and may include, as appropriate, the legal description of the site, survey information concerning the site, interior space requirements, special material requirements, material quality standards, conceptual criteria for the project, special equipment requirements, cost or budget estimates, time schedules, quality assurance and quality control requirements, site development requirements, applicable codes and ordinances, provisions for utilities, parking requirements, or any other requirement, as applicable.
In using that method and in entering into a contract for the services of a design-build firm, the contracting institution and the design-build firm shall follow the procedures provided by Subsections c - k. If the board's engineer or architect is not a full-time employee of the institution, any engineer or architect designated shall be selected on the basis of demonstrated competence and qualifications in accordance with Section The institution shall also prepare the design criteria package that includes more detailed information on the project.
If the preparation of the design criteria package requires engineering or architectural services that constitute the practice of engineering within the meaning of Chapter , Occupations Code, or the practice of architecture within the meaning of Chapter , Occupations Code, those services shall be provided in accordance with the applicable law. Each offeror must certify to the board that each engineer or architect that is a member of its team was selected based on demonstrated competence and qualifications in the manner provided by Section The board or its representative shall qualify a maximum of five offerors to submit additional information and, if the board or its representative chooses, to interview for final selection.
The board or its representative may request additional information regarding demonstrated competence and qualifications, considerations of the safety and long-term durability of the project, the feasibility of implementing the project as proposed, the ability of the offeror to meet schedules, costing methodology, or other factors as appropriate.
The board or its representative may not require offerors to submit detailed engineering or architectural designs as part of the proposal. The board or its representative shall rank each proposal submitted on the basis of the criteria specified in the request for qualifications.
The board or its representative shall select the design-build firm that submits the proposal offering the best value for the institution on the basis of the published selection criteria and on its ranking evaluations. The board or its representative shall first attempt to negotiate with the selected offeror a contract. If the board or its representative is unable to negotiate a satisfactory contract with the selected offeror, the institution shall, formally and in writing, end all negotiations with that offeror and proceed to negotiate with the next offeror in the order of the selection ranking until a contract is reached or negotiations with all ranked offerors end.
An architect shall have responsibility for compliance with the requirements of Chapter , Occupations Code. The institution shall select those services for which it contracts in accordance with Section If a fixed contract amount or guaranteed maximum price has not been determined at the time a design-build contract is awarded, the penal sums of the performance and payment bonds delivered to the institution shall each be in an amount equal to the project budget, as specified in the design criteria package.
The design-build firm shall deliver the bonds not later than the 10th day after the date the design-build firm executes the contract unless the design-build firm furnishes a bid bond or other financial security acceptable to the institution to ensure that the design-build firm will furnish the required performance and payment bonds when a guaranteed maximum price is established.
In using that method and in entering into a contract for the services of a construction manager-agent, a board shall follow the procedures prescribed by this section. An institution using the construction manager-agent method may, under the contract between the institution and the construction manager-agent, require the construction manager-agent to provide administrative personnel, equipment necessary to perform duties under this section, and on-site management and other services specified in the contract.
A construction manager-agent represents the institution in a fiduciary capacity. If the engineer or architect is not a full-time employee of the institution, the board shall select the engineer or architect on the basis of demonstrated competence and qualifications as provided by Section The institution's engineer or architect may not serve, alone or in combination with another person, as the construction manager-agent unless the engineer or architect is hired to serve as the construction manager-agent under a separate or concurrent procurement conducted in accordance with this subchapter.
This subsection does not prohibit the institution's engineer or architect from providing customary construction phase services under the engineer's or architect's original professional service agreement in accordance with applicable licensing laws. In using that method and in entering into a contract for the services of a construction manager-at-risk, a board shall follow the procedures prescribed by this section. The institution's engineer, architect, or construction manager-agent for a project may not serve, alone or in combination with another, as the construction manager-at-risk unless the engineer or architect is hired to serve as the construction manager-at-risk under a separate or concurrent procurement conducted in accordance with this subchapter.
The board shall select those services for which it contracts in accordance with Section The board shall prepare a request for proposals, in the case of a one-step process, or a request for qualifications, in the case of a two-step process, that includes general information on the project site, project scope, schedule, selection criteria, estimated budget, and the time and place for receipt of proposals or qualifications, as applicable, a statement as to whether the selection process is a one-step or two-step process, and other information that may assist the board in its selection of a construction manager-at-risk.
The board shall state the selection criteria in the request for proposals or qualifications, as applicable. The selection criteria may include the offeror's experience, past performance, safety record, proposed personnel and methodology, and other appropriate factors that demonstrate the capability of the construction manager-at-risk. If a one-step process is used, the board may request, as part of the offeror's proposal, proposed fees and prices for fulfilling the general conditions.
If a two-step process is used, the board may not request fees or prices in step one. In step two, the board may request that five or fewer offerors, selected solely on the basis of qualifications, provide additional information, including the construction manager-at-risk's proposed fee and its price for fulfilling the general conditions.
At the appropriate step, the board shall also read aloud the fees and prices, if any, stated in each proposal as the proposal is opened. Within 45 days after the date of opening the proposals, the board or its representative shall evaluate and rank each proposal submitted in relation to the criteria set forth in the request for proposals.
If the board or its representative is unable to negotiate a satisfactory contract with the selected offeror, the board or its representative shall, formally and in writing, end negotiations with that offeror and proceed to negotiate with the next offeror in the order of the selection ranking until a contract is reached or negotiations with all ranked offerors end.
A construction manager-at-risk may seek to perform major elements of the work itself if the construction manager-at-risk submits its bid or proposal for that work in the same manner as all other trade contractors or subcontractors and if the board determines that the construction manager-at-risk's bid or proposal provides the best value for the institution.
If no satisfactory bid or proposal for a major element of the work is received in the time allowed, the board may negotiate directly with the construction manager-at-risk for performance of that work. The board may negotiate directly with the manager-at-risk for the performance of minor elements of the work that are not included in major work packages. All bids or proposals shall be made public after the award of the contract or within seven days after the date of final selection of bids and proposals, whichever is later.
The construction manager shall deliver the bonds not later than the 10th day after the date the construction manager executes the contract unless the construction manager furnishes a bid bond or other financial security acceptable to the institution to ensure that the construction manager will furnish the required performance and payment bonds when a guaranteed maximum price is established.
June 20, ; Acts , 78th Leg. The selected or designated engineer or architect has full responsibility for complying with Chapter or , Occupations Code, as applicable.
The board shall state in the request for proposals the selection criteria that will be used in selecting the successful offeror. Within 45 days after the date of opening the proposals the board shall evaluate and rank each proposal submitted in relation to the published selection criteria. The board shall first attempt to negotiate with the selected offeror a contract. The board and its engineer or architect may discuss with the selected offeror options for a scope or time modification and any price change associated with the modification.
If the board is unable to reach a contract with the selected offeror, the board shall, formally and in writing, end negotiations with that offeror and proceed to the next offeror in the order of the selection ranking until a contract is reached or all proposals are rejected.
The order may be a fixed price, lump-sum contract based substantially on contractual unit pricing applied to estimated quantities or may be a unit price order based on the quantities and line items delivered. If the institution fails to advertise that term, the base term may not exceed two years and is not renewable without further advertisement and solicitation of proposals.
If the architect or engineer is not a full-time employee of the institution, the board shall select the architect or engineer on the basis of demonstrated competence and qualifications as provided by Section The board of an institution may not enter into a contract with a person relating to a permanent improvement project at the institution under which the institution makes contractual payments to the person that are not reflected on the institution's financial statement unless the board:.
In this subchapter, "general academic teaching institution," "governing board," "medical and dental unit," and "university system" have the meanings assigned by Section A general academic teaching institution shall admit first-time freshman students for each semester under the provisions of this subchapter.
If the number of applicants who qualify for automatic admission to The University of Texas at Austin under Subsection a for an academic year exceeds 75 percent of the university's enrollment capacity designated for first-time resident undergraduate students for that academic year, the university may elect to offer admission to those applicants as provided by this subsection and not as otherwise required by Subsection a.
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