Q. A particle executing S.H.M. of amplitude $4\ cm$ and $T = 4\ s.$ The time taken by it to move from positive extreme position to half the amplitude is
A) $1\ s$
B) $1/3\ s$
C) $2/3\ s$
D) $\sqrt{3/2}\ s$
Explanation
(c) Equation of motion $y = a\cos{\omega t}$
$\Rightarrow \frac{a}{2} = a\cos{\omega t \Rightarrow \cos{\omega t = \frac{1}{2} \Rightarrow \omega t = \frac{\pi}{3}}}$
$\Rightarrow \frac{2\pi t}{T} = \frac{\pi}{3} \Rightarrow t = \frac{\frac{\pi}{3} \times T}{2\pi} = \frac{4}{3 \times 2} = \frac{2}{3}s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.