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:

For SHM, maximum acceleration, amax = ω²a = α where a is the amplitude of SHM. and maximum velocity, vmax = ωa = β so, α/β = ω²a/ωa = ω or α/β = ω or ω = α/β The angular frequency ω is related to the time period T by the equation ω = 2π/T. Therefore, α/β = 2π/T which gives T = 2πβ/α