Physics - SHM Question with Solution | TestHub

The correct option is (B). Concept: For SHM, $\mathrm{a}=-\left({\omega }^2\right)\mathrm{x}$ is the necessary condition. A general solution for SHM can be written as, $x=A\sin (\omega t+\varphi )$ where, $\mathrm{x}$ is the displacement from mean position, $A$ is the amplitude, $\omega$ is the angular frequency and $\varphi$ is the phase angle. On taking the first derivative, velocity can be written as $$v=\frac{dx}{dt}=(A\omega )\cos (\omega t+f)=(Aw)\sin \left(\omega t+\varphi +\frac{\pi }{2}\right)$$ And, taking derivative of velocity, acceleration can be written as: $$\mathrm{a}=\frac{\mathrm{dv}}{\mathrm{dt}}=-\left(\mathrm{A}{\omega }^2\right)\sin (\omega \mathrm{t}+\varphi )=\left(\mathrm{A}{\omega }^2\right)\sin (\omega \mathrm{t}+\varphi +\pi )$$ Therefore, in SHM acceleration is ahead of velocity by a phase $\frac{\pi }{2}$ Hence, Option (B) is the only correct option.