Question

The displacement of a particle along the x-axis is given by x = a $si{n}^2$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

The correct option is A simple harmonic motion of frequency $\omega /\pi$

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

$x=\frac{a}{2}(1-cos2t)$

from the above equation

$\omega =2$

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

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