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$$A = A_0 e^{-\gamma t}$$

$$A = \dfrac{A_0}{2}$$ after 10 oscillations

$$\because $$ After 2 seconds

$$\dfrac{A_0}{2} = A_0 e^{-\gamma (2)}$$

$$2 = e^{2 \gamma}$$

$$\ell n 2 = 2 \gamma $$

$$\gamma = \dfrac{\ell n 2}{2}$$

$$\because A = A_0 e^{-\gamma t}$$

$$\ell n \dfrac{A_0}{A} = \gamma t$$

$$\ell n 1000 = \dfrac{\ell n 2}{2} t$$

$$2 \left(\dfrac{3 \ell n 10}{\ell n2} \right) = t$$

$$\dfrac{6 \ell n 10}{\ell n 2} = 1$$

$$t = 19.931 sec$$

$$t \approx 20 \, sec$$

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