Q. A simple harmonic oscillator has an amplitude $a$ and time period $T.$ The time required by it to travel from $x = a$ to $x = a/2$ is
A) $T/6$
B) $T/4$
C) $T/3$
D) $T/2$
Explanation
(a) It is required to calculate the time from extreme position
Hence, in this case equation for displacement of particle can be written as $x = a\sin{\left( \omega t + \frac{\pi}{2} \right) = a\cos{\omega t}}$
$\Rightarrow \frac{a}{2} = a\cos{\omega t \Rightarrow \omega t = \frac{\pi}{3}} \Rightarrow \frac{2\pi}{T}.t = \frac{\pi}{3} \Rightarrow t = \frac{T}{6}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.