$a=a_{0} \mathrm{e}^{-\mathrm{bt/m}}$              $...(i)$

Energy of vibration drop to half of its in itial value $\left(\mathrm{E}_{0}\right),$ as $\mathrm{E} \propto \mathrm{a}^{2} \Rightarrow \mathrm{a} \propto \sqrt{\mathrm{E}}$

$a=\frac{a_{0}}{\sqrt{2}} \Rightarrow \frac{b t}{m}=\frac{10^{-2} t}{0.1}=\frac{t}{10}$

From $eq^n(i),$

$\frac{a_{0}}{\sqrt{2}}=a_{0} e^{-t / 10}$

$\frac{1}{\sqrt{2}}=e^{-t / 10}$ or $\sqrt{2}=e^{\frac{t}{10}}$

$\ln \sqrt{2}=\frac{t}{10} \quad \therefore t=3.5$ seconds