A body of mass $20$ g is executing SHM with amplitude $5$ cm. When it passes through the equilibrium position its speed is $20$ cm/s. What would be the distance from equilibrium when its speed becomes $10$ cm/s?
1. $\frac{5\sqrt{3}}{4}$ cm

2. $\frac{5\sqrt{3}}{2}$ cm

3. $\frac{25\sqrt{7}}{2}$ cm

4. $5\sqrt{3}$ cm

For a simple harmonic oscillator, a velocity-time diagram is shown. The angular frequency of oscillation is:

1.  $\frac{24}{2}$ rad/s

2.  $\frac{25\mathrm{\pi }}{4}$ rad/s

3.  25 rad/s

4.  25$\mathrm{\pi }$ rad/s

In an S.H.M, when the displacement is one-fourth of the amplitude, the ratio of total energy to the potential energy is 

1.  16: 1

2.  1: 16

3.  1: 8

4.  8: 1

A particle executing S.H.M. Its displacement x varies with time t as $x=8\sin 4t+6\cos 4t.$  The maximum  velocity of the particle will be:

1.  20 unit

2.  10 unit

3.  40 unit

4.  5 unit

The amplitude of oscillation for a particle executing S.H.M with angular frequency $\mathrm{\pi }$rad/s and maximum acceleration $5{\mathrm{\pi }}^2 \mathrm{m}/{\mathrm{s}}^2$ is

1.  25 cm

2.  25 m

3.  5 cm

4.  5 m

Which of the following statements is true for an ideal simple pendulum?

A mass of $30~\text{gm}$ is attached with two springs having spring constants $100~\text{N/m}$ and $200~\text{N/m}$ and other ends of springs are attached to rigid walls as shown in the given figure. The angular frequency of oscillation is: 
(ground is smooth)
 

1. $\dfrac{100}{2\pi}~\text{rad/s}$
2. $\dfrac{100}{\pi}~\text{rad/s}$
3. ${100}~\text{rad/s}$
4. ${200}~\text{rad/s}$

If a bob of the simple pendulum having negative charge q is made to oscillate in a uniform electric field acting vertically upward direction, then its time period:

1.  Increases

2.  Decreases

3.  No effect of the electric field

4.  Decreases or increases

A simple pendulum of length l and bob of mass m is executing S.H.M with amplitude A. The maximum tension in the string will be

1.  $\mathrm{mg}\left(\frac{\mathrm{l}}{\mathrm{l} + \mathrm{A}}\right)$

2.  $\mathrm{mg}\left(\frac{{\mathrm{l}}^2 + {\mathrm{A}}^2}{{\mathrm{l}}^2}\right)$

3.  $\mathrm{mg}\left(\frac{{\mathrm{l}}^2}{{\mathrm{l}}^2 + {\mathrm{A}}^2}\right)$

4.  $\mathrm{mg}\left(\frac{\mathrm{l} + \mathrm{A}}{\mathrm{l}}\right)$