Mechanical Impedance Analysis
As a simple application, let's find the motion of the mass , after time zero, given that the input force is an impulse at time 0:
Thus, the impulse response of the mass oscillates sinusoidally with radian frequency , and amplitude . The velocity starts out maximum at time , which makes physical sense. Also, the momentum transferred to the mass at time 0 is ; this is also expected physically because the time-integral of the applied force is 1 (the area under any impulse is 1).