**Question:**

**What is the ratio of maximum acceleration to the maximum velocity of a simple harmonic oscillator?**

**Solution:**

The displacement equation of SHM is x = a sin (ꞷt + ϕ)

The velocity of the particle, v = dx/dt = d a sin (ꞷt + ϕ)/dt

Maximum velocity, |v|max = aꞷ

Acceleration, A = dv/dt = aꞷ2 sin (ꞷt + ϕ)

Maximum acceleration, |A|max = ꞷ2a

|v|max/|A|max = ꞷ