Question

The maximum acceleration of a simple harmonic oscillator is a₀, while the maximum velocity is v₀, what is the displacement amplitude?

Answer 1

Here, v₀ =  ωA, a₀ = ω²A = (ωA)ω = v₀ω

or v₀ω = a₀

ω = \(\frac{a_0}{v_0}\)

Thus  A = \(\frac{v_0}{ω}=\frac{v_0}{\frac{a_0}{v_0}}=\frac{v^2_0}{a_0}\)