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

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.

Answer 1

[Prajit T R]

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

[Neha Sinha]

Thank you