Physics - SHM Question with Solution | TestHub

Let when $m$ is hanging, the extension in the spring is $l$, then tension in the string is, $T_1=kl=mg$ when force is applied, let the further extension is x . The tension in the spring is $T_2=k(x+l)$ $\begin{array}{rl}& \therefore \text{ Driving force }=T_2-T_1=k(x+l)-kl=kx\\ & \therefore \text{ Acceleration }=\frac{kl}{m}\end{array}$ $\begin{array}{rl}\Rightarrow T& =2\pi \sqrt{\frac{\text{ displacement }}{\text{ acceleration }}}\\ & =2\pi \sqrt{\frac{x}{\frac{kx}{m}}}=2\pi \sqrt{\frac{m}{k}}\end{array}$