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. Find the effective spring constant.

3. 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?

4. 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.

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 block system is on a horizontal plane. If spring constant is 2N/m & mass of block is 1kg. By what amount should the block be extended from equilibrium position such that maximum velocity at mean position is 2m/s?

7. 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?

8. 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.

9. If the block is displaced by ‘x’ from the mean position, what will be the time period of oscillations?

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

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

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

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. What will happen to the time period of a simple pendulum if temperature of the surroundings is significantly increased?

15. What is the length of a seconds pendulum?