MATLAB: I want to envelope the damped curve with an exponential function passing through the peak points. Can someone help

curve

X = A1*(exp(-alpha*t)).*cos(wd*t)+ A2*(exp(-alpha*t)).*sin(wd*t) is the equation of the damped curve with parameters as t=0:0.000050:0.1; A1 = 12.87701558; A2 = -12.70012814; alpha = 67.91641; wd = 4770.680551
The equation of the enveloping curve is I = Io * exp(-67.91641*t) where Io is the peak values of the damped curve
I am attaching the image of damped curve as well as its enveloping curve through peak points.

Best Answer

Hi Neha
You can use the function 'envelop' to obtain the envelope of the curve. I am attaching the code below:
 plot(t,damped_curve);
 up = envelope(damped_curve);
 hold on;
 plot(t,up);
 hold off;
The documentation link for the function is here: https://www.mathworks.com/help/signal/ref/envelope.html
Prajit
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