Solution:
Amplitude after $n$ oscillations is given by $A = A_0 e^{-k n}$. For $n = 100$, $A_{100} = A_0 e^{-100k} = A_0 \frac{1}{3}$. For $n = 200$, $A_{200} = A_0 e^{-200k} = A_0 (e^{-100k})^2 = A_0 (\frac{1}{3})^2 = A_0 \frac{1}{9}$.
When an oscillator completes 100 oscillation its amplitude reduced to $\frac{1}{3}$ of initial value. What will be its amplitude, oscillation when it completes 200 oscillation? (2002)
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