Question

A simple harmonic oscillator has an amplitude a and time period T. The time required by it to travel from x = a to x = $\frac{a}{2}$ is

[CBSE PMT 1992; SCRA 1996; BHU 1997]

• A. T/6
• B. T/4
• C. T/3
• D. T/2

Answer 1

The correct option is A

T/6

It is required to calculate the time from extreme position.

Hence, in this case equation for displacement of particle can be written as

$x=asin(\omega t+\frac{\pi }{2})=acos\omega t$

$\Rightarrow \frac{a}{2}=acos\omega t\Rightarrow \omega t=\frac{\pi }{3}\Rightarrow \frac{2\pi }{T}.t=\frac{\pi }{3}\Rightarrow t=\frac{T}{6}$