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

(a) 1/8
(b) 2/3
(c) 1/6
(d) 1/9
Correct option: (d) 1/9
Given t = 100 T, a = a0/3
Let a’ be the amplitude after completing 200 oscillations, i.e. at t = 200 T.
a = a0/3 = a0e-100Tb
Also, a’ = a0e-200Tb
Therefore, a’ = a0/9
Thus, the ampitude reduces by 1/9th of the initial value.

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