Question

The maximum acceleration of a simple harmonic oscillator is a₀ and the maximum velocity is v₀. What is the displacement amplitude?

Answer 1

Let A be the displacement amplitude and ω be the angular frequency of S.H.M., Then,

Maximum velocity, v₀ = ωA; ω = v₀/A

Maximum acceleration,

\(a_0 = \omega^2\ A = (\frac{v_0}{A})^2\ A = \frac{v_0^2}{A}\)

∴ Displacement amplitude, A = \(\frac{v_0^2}{a_0}\)