How can I bulid the exponential envelope of a damped second-order system oscillator?

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Leonardo Molino 2022-6-9

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评论： Star Strider 2022-6-12

Hello everyone,

I have a signal made up of points that show the classic second-order system damped oscillations. I would like to build the exponential function that rules the amplitude decay and I did it roughly by interpolating the peaks with an ownmade function that works preatty well. Now the idea is to find out also the coefficients of the exponential decay, but I don't now how to apporach this problem.

I have the complete signal as well as the exponential envelope created by interpolation.

Thank you for the help.

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Star Strider 2022-6-9

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One option is presented in Damped harmonic motion curve fit where the exponential envelope function is one of the parameters the code estimates. If you want to do more than that, see Curve Fitting of large Data Measurement?.

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Leonardo Molino 2022-6-12

Thank you, I will try!

For the records, the equation to be solved is this one here, and rules the dynamics of an aircraft elevator.

The forcing terms are linear functions of the state vector.

I have sucessfully solved this problem with ode45, but as you have correctly said, the analytic expression might be a little bit different from the one of a "regular" pendulum.