Question

The maximum speed and acceleration of a simple harmonic oscillator are 0.92 m/s and 1.54 m/s2 . Find the oscillation amplitude.

Answer 1

for simple harmonic oscillator, displacement is given by

x = A*cos(wt)

where A is amplitude (maximum displacement)

velocity v = dx/dt

v = - Awsin(wt)

so maximum velocity Vmax = Aw

acceleration a = dv/dt = - Aw^2sin(wt)

so maximum acceleration a(max) = Aw^2

now A = (Vmax)^2/a(max)

amplitude A = (0.92)^2/1.54 = 0.549 m