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
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