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$ = ${\mathrm{\nu }}_1$

The plot of velocity (v) versus displacement (x) of a particle executing simple harmonic motion is shown in the figure. The time period of osciliation of the particle is:

(1) $\frac{\pi }{2} \mathrm{s}$

(2) $\pi$ s

(3) 2$\pi$ s

(4) 3$\pi$ s

The equation of simple harmonic motion may not be expressed as (each term has its usual meaning):

(1) $x=A\sin (\omega t+\varphi )$

(2) $x=A\cos (\omega t-\varphi )$

(3) $x=a\sin \omega t + b\cos \omega t$

(4) $x=A\sin (\omega t+\varphi )+B\sin (2\omega t+\varphi )$

If a particle is executing simple harmonic motion, then the acceleration of the particle:

(1) is uniform.

(2) varies linearly with time.

(3) is non-uniform.

(4) Both (2) & (3)

What is the phase difference between the acceleration and the velocity of a particle executing simple harmonic motion?

(1) Zero

(2) $\frac{\pi }{2}$

(3) $\pi$

(4) 2$\pi$

The shape of the graph plotted between the velocity and the position of a particle executing simple harmonic motion is:

(1) A straight line

(2) An ellipse

(3) A parabola

(4) A hyperbola 

If a particle is executing simple harmonic motion with time period T, then the time period of its total mechanical energy is:

(1) Zero

(2) $\frac{T}{2}$

(3) 2T

(4) Infinite