Fitting a damping function to a sinusoidal response
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I'm attempting to fit an exponential damping function to a sinusoidal wave by iterating zeta values.
However, it seems I can never get it to properlly 'ride' along the peaks, meaning it always crosses the response function (pic)
As I understand, the damping function looks like exp(-zeta*wn*t). I have estimated the value of wn and I have all values of time.
The function code looks like this:
xi1 = 0.01;
y = exp(-xi1*wn1*(time1-4.3))-0.6568;
I subtract 0.6568 to have the damping function begin on the first peak.