1. 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.

2. Consider the damped SHM of a spring mass system. If the time taken for the amplitude to become half is 'T', what is the time taken for mechanical energy to become half?

3. What is the amplitude of motion for x = 2sin(2t) + 4sin²t ?

4. The springs in the given diagram are fixed to the walls. If the block is displaced by a distance x from the mean position, find the time period of oscillations in seconds. Assume that there is no friction.

5. A spring block system is on a horizontal surface. The block is compressed by 10cm. What should be the coefficient of friction between the block and ground such that the block comes to a stop at the mean position? Mass of block = 0.5kg & spring constant = 3N/m.

6. 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?

7. Which of the following factors affects the time period of a simple pendulum?

8. 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?

9. Every periodic motion is oscillatory, but not vice versa. True or False?

10. Find the effective spring constant.

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

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

13. Damping force on a spring mass system is proportional to which of the following quantities?

14. A ball tied to the end of a string of length 10cm is rotated with constant speed of 2m/s in a circle about the origin. Find the equation of projection of the ball on the x-axis. At t=0, the ball makes an angle of 45° with the x-axis & is travelling in anticlockwise direction.

15. The curves given below are that of position(x), velocity(v) & acceleration(a) vs time. What can we infer about the value of angular frequency 'f' from the given curves?

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

17. 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?

18. Resonance occurs when frequency of forced oscillations is close to natural frequency. True or False?

19. 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?

20. 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.

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

22. 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?

23. Force on a particle is given by: F = -kxⁿ. For what values of n will the motion be oscillatory?

24. 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.

25. 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.