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Question:

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s⁻¹. At t = 0, the displacement is 5 m. What is the maximum acceleration?

750m/s2

500m/s2

750√2m/s2

500√2m/s2

Solution:

amax = Aω² (1)
Vmax = Aω
Now, amax/Vmax = Aω²/Aω = ω
i.e = ω = 10
displacement = A cos(ωt + θ) = A cos(0 + θ) = A cos(θ)
5 = A/(√2) ⇒ A = 5√2
Now amax = 5√2 × 10² from (1)
= 10 × 5√2 = 500√2 m/s²