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.  $\frac{2\mathrm{A}}{\sqrt{3}}$

A particle is performing SHM with amplitude \(A\) and angular velocity \(\omega.\) The ratio of the magnitude of maximum velocity to maximum acceleration is:
1. \(\omega\)
2. \(\dfrac{1}{\omega }\)
3. \(\omega^{2} \)
4. \(A\omega\)

The potential energy of a particle executing SHM is 2.5 J when its displacement is half of the amplitude. The total energy of the particle is:

1.  18 J

2.  10 J

3.  12 J

4.  2.5 J