Physics - SHM Question with Solution | TestHub

Let, $\mathrm{x}=\mathrm{A}\sin \omega \mathrm{t}$ $\mathrm{v}=\frac{\mathrm{dx}}{\mathrm{dt}}=\mathrm{A}\omega \cos \omega \mathrm{t}$ Kinetic energy, $\mathrm{K}=\frac{1}{2}{\mathrm{mv}}^2$ $\begin{array}{rl}& \Rightarrow \mathrm{K}=\frac{1}{2}\mathrm{m}{\omega }^2{\mathrm{A}}^2{\cos }^2\omega \mathrm{t}\\ & \Rightarrow \mathrm{K}=\frac{1}{2}\mathrm{m}{\omega }^2{\mathrm{A}}^2\left(\frac{1+\cos 2\omega \mathrm{t}}{2}\right)\\ & \Rightarrow \mathrm{K}=\frac{1}{4}\mathrm{m}{\omega }^2{\mathrm{A}}^2\left(1+{\cos }^2\omega \mathrm{t}\right)\\ & \therefore {\omega }_{\mathrm{K}}=2\omega \end{array}$ $\therefore$ Frequency of oscillation of $\mathrm{K}.\mathrm{E}=2\mathrm{f}\left[\mathrm{f}=\frac{\omega }{2\pi }\right]$