A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then, its time period of vibration will be

If  A  and ω  be amplitude and angular frequency of  vibration, thenα=ω2A                    . . . . (i) and β=ωA          . . . . .(ii)Diving eqn. (i) by eqn. (ii), we getαβ=ω2AωA=ω∴   Time period of vibration is T=2πω=2π(α/β)=2πβα