Question

Displacement of particle along x-axis by $x=a{\sin }^2\omega t$. Its motion is SHM of frequency :

• A. $\omega /\pi$
• B. $3\omega /2\pi$
• C. $\omega /2\pi$
• D. $notSHM$

Answer 1

The correct option is D $notSHM$

We have,

$x=a{\sin }^2\omega t$

$\Rightarrow \frac{dx}{dt}=2\omega \left(\sin \omega t\right)\left(\cos \omega t\right)$

$\Rightarrow \frac{d^{2}x}{d{t}^2}=2\omega ({\cos }^2\omega t-{\sin }^2\omega t)$

$\Rightarrow a=2a{\omega }^2\cos 2\omega t$

But for SHM,

$a\propto -{\omega }^2$

So, This is not $SHM$.

So, the correct option will be $\left(D\right)$