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Question

In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be

A
a02
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B
a04
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C
a06
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D
a09
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Solution

The correct option is D a09
In damped oscillation, amplitude goes on decaying exponentially.
i.e a=a0eγt where γ = damping coefficient.
Given, a03=a0eγ×100T
where T = time period of one oscillation
or 13=e100 γT......(i)
After 200 oscillations,
a=a0eγ×200 T
or a=a0[e100 γT]2
or a=a0×[13]2 [From Eq. i]
or a=a09

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