A general graph showing variation in the potential energy \((P.E)\) of a particle with time while executing S.H.M. is:

1.		2.
3.		4.

Two simple pendulums of lengths 1.44 m and 1 m start S.H.M. together in the same phase. They will be in the same phase again after

1.  6 vibrations of the longer pendulum

2.  6 vibrations of the smaller pendulum

3.  5 vibrations of the smaller pendulum

4.  4 vibrations of the longer pendulum

A spring has equilibrium elongation 0.1 m when suspended vertically with a load. If the load is slightly displaced vertically downward and released, then the time period of SHM of the system will be approximately

1.  0.1 s

2.  0.4 s

3.  0.6 s

4.  0.3

Select the correct statements regarding potential energy \((U)\) in the simple harmonic motion of a particle along \(x\text-\)axis:

A simple pendulum is pushed slightly from its equilibrium towards the left and then set free to execute the simple harmonic motion. Select the correct graph between its velocity (\(v\)) and displacement (\(x \)).

1.		2.
3.		4.

Simple harmonic motion is an example of:

A particle under SHM takes 1.2 s to complete one vibration. Minimum time taken by it to travel from mean position to half of its amplitude is

1.  0.2 s

2.  0.1 s

3.  0.4 s

4.  0.3 s

The potential energy of a particle executing SHM at the extreme position and mean position are 20 J and 5 J respectively. The kinetic energy of the particle at the mean position is:

1.  20 J

2.  5 J

3.  15 J

4.  12.5 J

Equation of simple harmonic motion of a particle is y = (0.4 m) sin314t, where time t is in second. Frequency of vibration of the particle is

1.  100 Hz

2.  75 Hz

3.  50 Hz

4.  25 Hz

A particle starts SHM from the mean position. Its amplitude is A and time period is T. At the time when its speed is half of its maximum speed, its displacement is

1.  $\frac{\mathrm{A}}{2}$

2.  $\frac{\mathrm{A}}{\sqrt{2}}$

3.  $\frac{\mathrm{A}\sqrt{3}}{2}$

4.  $\frac{2\mathrm{A}}{\sqrt{3}}$