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Topic 10 : Domped Oscillation

1. ⇒ (AIPMT 2003)

In case of a forced vibration, the resonance peak becomes very sharp when the

A. damping force is small

B. restoring force is small

C. applied periodic force is small

D. quality factor is small

Correct Answer is Option (A)

The resonance wave becomes very sharp when damping force is small.

2. ⇒ (AIPMT 2002)

When an oscillator completes 100 oscillations its amplitude reduced to 1 3 of initial value. What will be its amplitude, when it complettes 200 oscillations ?

A. 1 8

B. 2 3

C. 1 6

D. 1 9

Correct Answer is Option (D)

This is a case of damped vibration as the amplitude of vibration is decreasing with time.
Amplitude of vibrations at any instant t is given by a = a 0 e b t , where a 0 is the initial amplitude of vibrations and b is the damping constant.

Now, when t = 100T, a = a 0 / 3   [T is time period]

Let the amplitude be a at t = 200T.
i.e. after completing 200 oscillations.

a = a 0 / 3 = a 0 e 100 T b    ...(i)

and a = a 0 e 200 T b ...(ii)

From (i), 1 3 = e 100 T b
e 200 T b = 1 / 9

From (ii), a = a 0 × 1 9 = a 0 9

The amplitude will be reduced to 1/9 of initial value.