Physics - SHM Question with Solution | TestHub

Let displacement be$x=A\sin \left(\omega t+\varphi \right)$

Kinetic energy,$K=\frac{1}{2}m{\omega }^2{A}^2{\cos }^2\left(\omega t+\varphi \right)$

As the average value of${\cos }^2\left(\omega t+\varphi \right)$over a cycle is$\frac{1}{2}$.

Therefore average kinetic energy is$K_{\mathrm{a}\mathrm{v}}=\frac{1}{4}m{\omega }^2{A}^2$