Fitting a damping function to a sinusoidal response

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;

plot(time1-4.3,Response1)
hold on
plot(time1-4.3,y)
hold off
grid on

I subtract 0.6568 to have the damping function begin on the first peak.

Answer 1

[Image Analyst]

Try using findpeaks(), and then just pass the peak locations into fitnlm(), like in my attached demo.

Answer 2

[Star Strider]

See: Damped harmonic motion curve fit