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

Answer

A

Explanation

Maximum acceleration
`alpha=Aomega^(2)` . . (1)
Maximum velocity
`beta=A omega`
`(Eq^(n)(1))/(Eq^(n)(2))implies(alpha)/(beta)implies(alpha)/(beta)=(2pi)/(T)`
`T=2pi(beta)/(alpha)`