Question

The displacement of a particle along the x-axis is given by $x=as{in}^2\omega t$. The motion of the particle comes ponds to

• A. SHM of frequency $\frac{2\omega }{2\pi }$
• B. SHM of frequency $\frac{3\omega }{2\pi }$
• C. non SHM
• D. SHM of frequency $\frac{\omega }{2\pi }$

Answer 1

The correct option is A SHM of frequency $\frac{2\omega }{2\pi }$

Given that

$x=asi{n}^2\omega t$

this can be written as

$x=a\left[\frac{1-cos2\omega t}{2}\right]$

$x=\frac{a}{2}-\frac{a}{2}cos\omega t$

so from the above equation frequency of SHM is

$frequency=\frac{2\omega }{2\pi }$