Fourier HW Problem

 

Starting frequency [Hz]. Default is A3 below C4 (middle C).

MUTE  Play current wave

Play Square Wave

Find the steady-state motion of a damped harmonic oscillator that is driven by a periodic square wave force with a frequency w equal to 1/3 the natural frequency of the undamped oscillator.  Note that you don't really need to use the physlet above: it's only there for your reference.

Define the driving force in the following way:

F(t) =  F0/2 for 0 < wt < p, 2p < wt < 3p, etc.

F(t) = -F0/2 for p < wt < 2p, 3p < wt < 4p, etc

1. Show that the Fourier series expansion for the driving force is:

 

2. Find the relative amplitudes for the first 3 terms of the response function x(t).  Let the quality factor Q = 100.