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 gm is attached with two springs having spring constants 100 N/m and 200 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.  $\frac{100}{2\mathrm{\pi }}$ rad/s 

2.  $\frac{100}{\mathrm{\pi }}$ rad/s

3.  100 rad/s

4.  200$\mathrm{\pi }$ 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.  $\mathrm{mg}\left(\frac{\mathrm{l} + \mathrm{A}}{\mathrm{l}}\right)$

Find the percentage change in time period if the length of a simple pendulum is increased by 3% 

1.  3%

2.  6%

3.  1.5%

4.  2.5%

A disc is oscillating about a horizontal axis passing through its rim and perpendicular to the plane of the disc. If the radius of the disc is R, then the frequency of oscillation is

1.  $2\mathrm{\pi }\sqrt{\frac{3g}{2R}}$

2.  $2\mathrm{\pi }\sqrt{\frac{2\mathrm{R}}{3\mathrm{g}}}$

3.  $\frac{1}{2\mathrm{\pi }}\sqrt{\frac{3\mathrm{R}}{2\mathrm{g}}}$

4.  $\frac{1}{2\mathrm{\pi }}\sqrt{\frac{2\mathrm{g}}{3\mathrm{R}}}$

The amplitude of a damped oscillator becomes one-third in 10 minutes and $\frac{1}{\mathrm{n}}$ times of the original value in 30 minutes. The value of n is:

1.  81

2.  3

3.  9

4.  27

A particle is executing SHM with time period T. The time taken by it to travel from mean position to $\frac{1}{\sqrt{2}}$ times its amplitude is equal to

1.  $\frac{\mathrm{T}}{6}$

2.  $\frac{\mathrm{T}}{12}$

3.  $\frac{\mathrm{T}}{8}$

4.  $\frac{\mathrm{T}}{4}$