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 2 t )$
from the above equation $\omega=2$
frequency $=\frac{\omega}{2 \pi}$
frequency $=\frac{\omega}{\pi}$