A simple pendulum is attached to the roof of a lift. If the time period of oscillation, when the lift is stationary is T, then the frequency of oscillation when the lift falls freely, will be?

A.

Zero

B.

T

C.

1/T

D.

∞

Answer: Option A

Explanation:

In a freely falling lift, g=0 v=1/2π×√(g/l)=1/2π×√(0/l)=0.

A lightly damped oscillator with a frequency v is set in motion by a harmonic driving force of frequency v’. When v’ is lesser than v, then the response of the oscillator is controlled by?

A.

Spring constant

B.

Inertia of the mass

C.

Oscillator frequency

D.

Damping coefficient

Answer: Option A

Explanation:

Frequency of driving force is lesser than frequency v of a damped oscillator. The vibrations are nearly in phase with the driving force and response of the oscillator is controlled by spring constant.

Which of the following functions represents a simple harmonic oscillation?

A.

sinωt-cosωt

B.

sinωt+sin^{2}ωt

C.

sinωt-sin^{2}ωt

D.

sin^{2} ωt

Answer: Option A

Explanation:

y=sinωt-cosωt dy/dt=ωcosωt+ωsinωt (d^{2} y)/dt^{2} =-ω^{2} sinωt+ω^{2} cosωt =-ω^{2} (sinωt-cosωt) a=-ω^{2} y that is a∝y This satisfies the condition of simple harmonic motion.