A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is (a) 5 cm (b) 3 cm (c) 0 cm.
A = 5 cm = 0.05 m T = 0.2 s ω=2π/T=2π/0.2=10πrad/s When displacement is y, then acceleration, a=−ω2y Velocity, V=ωr2−y2 Case (a) When y=5cm=0.05m a=−(10π)2×0.05=−5π2m/s2 V=10π×(0.05)2−(0.05)2=0 Case (b) When y=3cm=0.03m a=−(10π)2×0.03=−3π2m/s2 V=10π×(0.05)2−(0.03)2=10π×0.04=0.4π m/s Case (c) When y=0 a=−(10π)2×0=0 V=10π×(0.05)2−02=10π×0.05=0.5πm/s
