Physics - SHM Question with Solution | TestHub

Let $a_0$ be the initial amplitude and $b$ be the damping constant The used formula is $a=a_0{e}^{-bt}$ In Ist case : $t=100T$ and $a=\frac{a_0}{3}$ $\therefore \frac{a_0}{3}=a_0{e}^{-b(100T)}$ $\begin{array}{rl}& \Rightarrow e^{-b\times 100T}=\frac{1}{3}\\ & \text{In 2nd case : }t=200T\\ & a=a_0{e}^{-200bT}\\ & \Rightarrow a=a_0{\left(e^{-100bT}\right)}^2\\ & \Rightarrow a=a_0{\left(\frac{1}{3}\right)}^2\\ & \Rightarrow a=\frac{a_0}{9}\end{array}$