A particle is performing simple harmonic motion. If its velocities are v1 and v2 at the displacements from the mean position arc y1 and y2 respectively, then its time period is

Velocity of a particle in SHM v = ωA2-y2v1 = ωA2-y12    ⇒v21 = ω2A2-ω2y21...(i)and v2 = ωA2-y22   ⇒ v22 = ω2A2-ω2y22-----(ii)from equations (i) and (ii), we getv22-v21 = ω2(y12-y22)ω = v22-v21y21-y22   ⇒ T = 2πω = 2πy21-y22v22-v21