Oscillation: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Oscillation. Understanding the underlying formula is key to arriving at the correct answer below:

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 $n = 200$, $A_{200} = A_0 e^{-200k} = A_0 (e^{-100k})^2 = A_0 (\frac{1}{3})^2 = A_0 \frac{1}{9}$.