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