Question

The displacement of a particle is represented by the

Equation y = 3 cos $\left( \frac{\pi}{4} - 2\omega t \right)$.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 $y = 3\cos\left( \frac{\pi}{4} - 2\omega t \right)$

$y = 3\cos\left\lbrack - \left( 2\omega t - \frac{\pi}{4} \right) \right\rbrack$

$= 3\cos\left( 2\omega t - \frac{\pi}{4} \right)$ [$\because\cos( - \theta) = \cos\theta$]

It represents simple harmonic motion with time period $T = \frac{2\pi}{2\omega} = \frac{\pi}{\omega}$