A particle is moving in SHM in a straight line. When the distance of the particle from equilibrium position has values `x_(1)` and `x_(2)` , the corresponding values of velocities are `u_(1)` and `u_(2)`. Show that time period of vibration is `T=2pi[(x_(2)^(2)-x_(1)^(2))/(u_(1)^(2)-u_(2)^(2))]^(1//2)`

Explanation

`T = 2pi ((x_(2)^(2) - x_(1)^(2))/(v_(1)^(2) - v_(2)^(2)))^(1//2)`