Question

The variation of the velocity of a particle executing SHM with time is shown in the figure. Find the velocity of the particle after a phase change of $\pi /6$ that takes place from the instant it is at one of the extreme positions.

Answer 1

Time period of oscillation =Time between two consecutive minima

$=2\times 2=4sec$

In one complete period phase change occurs by $2\pi$

The particle is at extreme position at $t=0s,2s,4s...$

So, change of phase $\frac{\pi }{6}$ associate with time interval

$=\frac{\frac{\pi }{6}}{2\pi }\times T=\frac{T}{12}=\frac{4}{12}=\frac{1}{3}sec$

So, change of phase $\frac{\pi }{6}$ occurs at $\frac{1}{3}sec$ after starting of motion.