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

Answer: (B)

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