1. A particle has an equation of motion given by: x = cos²wt – sin²wt. Select the correct statement regarding the same.

2. What happens to the energy of a particle, in SHM, with time in the presence of damping forces?

3. A particle is executing SHM and currently going towards the amplitude. If it is at A/2, what is the relation between the direction of velocity and acceleration?

4. A particle starts from the extreme position, at t = 0, in a SHM. If the time period of motion is 2s & maximum speed is 5m/s, find the equation of motion.

5. Consider a particle undergoing an SHM of amplitude A & angular frequency w. What is the magnitude of displacement from the mean position when kinetic energy is equal to the magnitude of potential energy?

6. A spring is fixed to the ground as shown below. A block of mass m is fixed to the spring. The spring is compressed by 5cm. Imagine that we can remove the spring suddenly and the block will fly off with the speed it has at that instant. The spring has to be removed at such a position that the distance travelled upwards by the block relative to that position is maximum. Find that position.

7. If the total energy of a particle in SHM is 200J, the value of kinetic energy at an instant can be 220J. True or False?

8. A spring mass system is hanging from the ceiling of a lift. It has been like this for quite some time. Suddenly the cables holding the lift are cut. What will be the amplitude of oscillation of the block when observed by a person standing (of mass M) in the lift?

9. The force acting on a particle of mass 1kg is -2x, where x is the displacement from the mean position of SHM. What is the time period of oscillations?

10. The angular speed of a body in uniform circular motion is the same as the angular frequency of SHM of its projection. True or False?

11. A particle is undergoing SHM. If its potential energy is given by: U = kx². What will be the value of x for potential energy to be 1/3rd of kinetic energy? Assume k is force constant.

12. Which of the following describes circular motion?

13. A spring mass system is on a horizontal plane. Spring constant is 2N/m & mass of block is 2kg. The spring is compressed by 10cm and released. A small ball is released from a height of 2m above the block on the horizontal plane. At what time should the ball be left if the block is released from the extreme position at t=0, given that the ball has to fall on the block when the speed of block is maximum?

14. A particle in uniform circular motion is projected on its diameter. The motion of projection will be simple harmonic. Select the correct option regarding speed and acceleration of the particle in circular motion.

15. A simple pendulum,hanging from the ceiling, is released from an angle . What is the restoring force?

16. Two simple pendulums of the same length are released from 10° & 20° respectively. Select the correct statement.

17. A force given by: F = -2(x – 1)²acts on a particle at rest. Select the correct option regarding the same.

18. A displacement function is given by: x = exp(sin2t). It is periodic. True or False?

19. The graph given below represents motion of what? And what type of motion is it? Assume that the downward direction in the graph is negative. Also find the value of t. Assume no loss of energy anywhere. Assume disp =0 implies ground level.

20. If a body in uniform circular motion covers the given angle in 0.5s, what is the time period of projection, on the x-axis, undergoing SHM? Assume it moves anti-clockwise.

21. Two springs in horizontal spring mass systems have spring constants in the ratio 2:3. By what ratio should they be extended from their mean positions so that they have the same value of maximum speed? The masses of blocks are the same in both cases.

22. Let T1 be the time period of a single spring mass system on a horizontal surface. Let T2 be the time period of the same system when hung from the ceiling. What is the expression for T1 & T2?

23. Force on particle, of mass 'm', undergoing SHM is given by: F = -kx. What is the relation between x and angular frequency w?

24. A particle is undergoing SHM with amplitude 10cm. The maximum speed it achieves is 1m/s. Find the time it takes to reach from the mean position to half the amplitude.

25. A ball is thrown up with a velocity of 2.5m/s. It collides elastically with the ground. Find the frequency of this periodic motion.