Physics - SHM Question with Solution | TestHub

The correct option is (D). Concept: For SHM, $\mathrm{a}=-\left({\omega }^2\right)\mathrm{x}$ is the necessary condition. A general solution for SHM can be written as, $\mathrm{x}=\mathrm{A}\sin (\omega \mathrm{t}+\varphi )$ where, $\mathrm{x}$ is the displacement from mean position, $\mathrm{A}$ is the amplitude, $\omega$ is the angular frequency and $\varphi$ is the phase angle. On taking the first derivative, velocity can be written as $\mathrm{v}=\frac{\mathrm{dx}}{\mathrm{dt}}=(\mathrm{A}\omega )\cos (\omega \mathrm{t}+\varphi )$ So, the maximum speed is $(\mathrm{A}\omega )=\mathrm{V}$. For average speed, over one-time interval $\mathrm{T}$, the body undergoing SHM moves by distance 4A. Thus, the average speed is given by $⟨|v|⟩=\frac{4\mathrm{A}}{\mathrm{T}}=\frac{4\mathrm{A}}{\left\{\frac{2\pi }{\left(\frac{\mathrm{v}}{\mathrm{A}}\right)}\right\}}=\frac{2\mathrm{V}}{\pi }$