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

Select the wrong statement about simple harmonic motion.

(1) The body is uniformly accelerated.

(2) The velocity of the body changes smoothly at all instants.

(3) The amplitude of oscillation is symmetric about the equilibrium position.

(4) The frequency of oscillation is independent of amplitude.