Math Challenge for you math geeks.

cjl said:

We have a winner!

(I'm assuming you got the response right - I don't feel like checking at the moment, but the physical system is definitely correct)

Click to expand...

The magnitude and phase of the response are probably wrong, but the natural frequency and damping factor are correct. Because you didn't have a forcing function, I estimated the response by inspection, first divide by 2, then it's in the Laplace tranform solution: s^2+2d*w_n*s+w_n^2=0. This gives: w_n^2 = 4 and 2d*w_n = 2. So, natural frequency w_n=2 and damping factor d=1/2. The damped frequency is w_d=w_n*sqrt(1-d^2)=2*sqrt(3/4)=sqrt(3)~=1.73. The time-domain response is in the form: C exp(-d*w_n*t)cos(w_d*t + theta), where C and theta depend on the initial conditions, which I don't remember how to apply off the top of my head. So, C exp(-t)cos(1.73t + theta).