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

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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.

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Prajit T R
Prajit T R 2018년 6월 29일
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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