Question

A particle executing S.H.M. of amplitude 4 cm and T = 4 sec. The time taken by it to move from positive extreme position to half the amplitude is

• A. 1 sec
• B. 1/3 sec
• C. 2/3 sec
• D. $\sqrt{3/2}$sec

Answer 1

Answer: (C)

2/3 sec

Answer 2

Equation of motion$y = a\cos\omega t$

⇒ $\frac{a}{2} = a\cos\omega t \Rightarrow \cos\omega t = \frac{1}{2} \Rightarrow \omega t = \frac{\pi}{3}$

$\Rightarrow \frac{2\pi t}{T} = \frac{\pi}{3} \Rightarrow t = \frac{\frac{\pi}{3} \times T}{2\pi} = \frac{4}{3 \times 2} = \frac{2}{3}\sec$