A body moving in a straightlint OAB with simple harmonic motion has zero velocity when at the points A and B whose distances from O and 'a' and 'b' respectively and has velocity v when half way between them. Find the period of the simple harmonic motion.

Explanation

In this ismple harmonicmotino, mean position is at C, figure . the amplitude of this SHM is,
`r=AC=CD=(AB)/(2)=(b-a)/(2)`
The velocity at the mean position,
`v=romega=((b-a)/(2))(2pi)/(T):.T=(pi(b-a))/(v)`