Question

The displacement of a particle is represented by the equation $ y = 3\,cos (\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

Answer: (B)

Given : $y = 3\,cos (\frac{\pi}{4}-2\omega t)$
$ y = 3\,cos [- (2\omega t - \frac{\pi}{4})]$
$=3\, cos (2\omega t - \frac{\pi}{4})$
$[\because cos (\theta) = cos \theta]$
It represents simple harmonic motion with time period
$T = \frac{2\pi}{2\omega}$
$= \frac{\pi}{\omega}$.