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? The initial phase is π 4 .

Step-by-step solution

In a simple harmonic motion, Maximum acceleration, f m a x = ω 2 A Maximum velocity, v max = A ω . f max v max = ω 2 A A ω = ω ω = 10 Displacement in SHM is x = A sin ⁡ ωt + π 4 At t = 0 5 = A sin ⁡ π 4 A = 5 2 . Max acceleration = ω 2 A = 100 × 5 2 = 500 2    m   s - 2