Question

The displacement of a particle is represented by the equation $y=3cos[\frac{\pi }{4}-2\omega t]$. The motion of the particle is:

• A. simple harmonic with period $\frac{2\pi }{\omega }$
• B. simple harmonic with period $\frac{\pi }{\omega }$
• C. periodic but not simple harmonic
• D. non - periodic.

Answer 1

The correct option is B simple harmonic with period $\frac{\pi }{\omega }$

Given: $y=3cos[\frac{\pi }{4}-2\omega t]$

$y=3cos[-[2\omega t-\frac{\pi }{4}\left]\right]=3cos[2\omega t-\frac{\pi }{4}]$

It represents simple harmonic motion with time period.

$T=\frac{2\pi }{2\omega }=\frac{\pi }{\omega }$.