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)

simple harmonic with period $\frac{\pi}{\omega}$

Answer 2

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