A body executes 40 oscillations/min.Its max. speed is 36cms-1,calculate the amplitude?

Question

A body executes 40 oscillation per minute. Its maximum speed is 36 cm/ s. Calculate amplitude of oscillation?

Answer 1

The formula for displacement in simple harmonic motion is: 

x = A sin (ωt) 

The derivative would therefore give speed: 
x' = Aωcos (ωt) 

The maximum speed is when cos(ωt) is at the maximum or 1. So max speed is: 
v(max) = Aω
36cm/s = A ((40 oscillations/minute) * (1 minute/second) * (2π/1 oscillation)) 
A = 36cm s^-1 / 4.188s^-1 
Amplitude A = 8.59 cm.