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

Options

A. `(beta^(2))/(alpha)`
B. `(2pibeta)/(alpha)`
C. `(beta^(2))/(alpha^(2))`
D. `(alpha)/(beta)`

Explanation

If A and `omega` be amplitude and angular frequency of vibration, then
`alpha=omega^(2)A" "…(i)`
and `beta=omegaA" "…(ii)`
Dividing eqn. (i) by eqn. (ii), we get
`(alpha)/(beta)=(omega^(2)A)/(omegaA)=omega`
`therefore` Time period of vibration is
`T=(2pi)/(omega)=(2pi)/((alpha//beta))=(2pibeta)/(alpha)`