Question

The displacement of a particle along the $x$ axis is given by $x=a{\sin }^2\omega t$. The motion of the particle corresponds to

• A. simple harmonic motion of frequency $\omega /\pi$
• B. simple harmonic motion of frequency $3\omega /2\pi$
• C. non simple harmonic motion
• D. simple harmonic motion of frequency $\omega /2\pi$

Answer 1

Answer: (A)

$x={\text{asin}}^{2}t$
$x=\frac{a}{2}(1-\cos 2t)$
from the above equation $\omega =2$
frequency $=\frac{\omega }{2\pi }$
frequency $=\frac{\omega }{\pi }$