A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 sec. What is the acceleration of the body when the displacement is 5 cm?
1. −3π² ms⁻²
2. 5π² ms⁻²
3. −5π² ms⁻²
4. 3π² ms⁻²

A body describes simple harmonic motion with an amplitude of \(5~\text{cm}\) and a period of \(0.2~\text{s}\). What is the velocity of the body when the displacement is \(3~\text{cm}\)?
1. \(0.4\pi ~\text{m/s}\)
2. \(0\)
3. \(0.5\pi ~\text{m/s}\)
4. \(0.3\pi ~\text{m/s}\)

A mass attached to a spring is free to oscillate, with angular velocity \(\omega\), in a horizontal plane without friction or damping. It is pulled to a distance${}_{}$ \(x_0\) and pushed towards the centre with a velocity \(v_0\) at time \(t=0\). The amplitude of the resulting oscillations is:
1. \(\sqrt{\left(2x_0^2+\frac{v_0^2}{\omega^2}\right)} \)
2. \(\sqrt{\left(x_0^2+\frac{v_0^2}{\omega^2}\right)} \)
3. \(\sqrt{\left(x_0^2+\frac{v_0^2}{2\omega^2}\right)} \)
4. \(\sqrt{\left( x_0^2+\frac{v_0^2}{\pi\omega^2}\right)} \)

Identify the correct definition:

The displacement of a particle executing S.H.M. is given by x = 0.01sin100$\pi$(t + 0.05). The time period is:

(1) 0.01 s

(2) 0.02 s

(3) 0.1 s

(4) 0.2 s

A boy is swinging in a swing. If he stands, the time period will:

(1) First decrease, then increase

(2) Decrease

(3) Increase

(4) Remain same

The time period of a simple pendulum in a freely falling lift will be:

(1) Finite

(2) Infinite

(3) Zero

(4) All of these

If the effective length of a simple pendulum is equal to the radius of the earth (R), the time period will be:

(1) $T=\pi \sqrt{\frac{R}{g}}$

(2) $T=2\pi \sqrt{\frac{2R}{g}}$

(3) $T=2\pi \sqrt{\frac{R}{g}}$

(4) $T=2\pi \sqrt{\frac{R}{2g}}$

A body executing S.H.M. along a straight line has a velocity of 3 ms^-1 when it is at a distance of 4 m from its mean position and 4 ms^-1 when it is at a distance of 3 m from its mean position. Its angular frequency and amplitude are:

(1) 2 rad s^-1 & 5 m

(2) 1 rad s^-1 & 10 m

(3) 2 rad s^-1 & 10 m

(4) 1 rad s^-1 & 5 m

The frequency of oscillation of a mass m suspended by a spring is ${\mathrm{\nu }}_1$. If the length of the spring is cut to one third, then the same mass oscillates with a frequency ${\mathrm{\nu }}_2$_, then:

(1) ${\mathrm{\nu }}_2$ = 3${\mathrm{\nu }}_1$

(2) 3${\mathrm{\nu }}_2$ = ${\mathrm{\nu }}_1$

(3) ${\mathrm{\nu }}_2$ = $\sqrt{3}$${\mathrm{\nu }}_1$

(4) $\sqrt{3}$${\mathrm{\nu }}_2$ = ${\mathrm{\nu }}_1$