Physics - SHM Question with Solution | TestHub

Given, $X={\mathrm{asin}}^2\omega t$ or $X=a\left(\frac{1-\cos 2\omega t}{2}\right)\left[\because \cos 2\theta =1-2{\sin }^2\theta \right]$ or $X=\frac{a}{2}-\frac{a\cos 2\omega t}{2}$ Now, $V=\frac{dx}{dt}=a\omega \sin 2\omega t$ and $a=dv/dt=2a{\omega }^2\cos 2\omega t$ Here, $a$ is not directly proportional to $(-x)$ which is a condition for SHM.