Physics - SHM Question with Solution | TestHub

In SHM, the acceleration of vibrating particle is proportional to displacement $$\begin{array}{rl}|\mathbf{a}|& ={\omega }^{2}x\\ \text{ Here }a=16\mathrm{cm}/{\mathrm{s}}^2& \\ & =16\times 10^{-2}\mathrm{m}/{\mathrm{s}}^2\end{array}$$ Displacement, $x=4\mathrm{cm}=4\times 10^{-2}\mathrm{m}$ $\therefore 16\times 10^{-2}={\omega }^2\left(4\times 10^{-2}\right)$ $$\begin{array}{rl}{\omega }^2& =4\\ \omega & =\pm 2\mathrm{rad}/\mathrm{s}\\ \omega & =\frac{2\pi }{T}\\ T& =\frac{2\pi }{\omega }=\frac{2\pi }{2}=\pi =3.142\mathrm{s}\end{array}$$