Parameters of a Damped Oscillator

[JohnRudnicki]

I want to estimate the parameters for a damped oscillator from an observed output (assuming the system acts like a damped oscillator). The attached evaluates the solution for a damped oscillator with zero initial conditions and a forcing function that ramps up to a unit value then ramps down to zero. And gives an example for assumed damping, etc. But I am interested in the inverse problem: Given only the output, how can I estimate or infer the parameters of the oscillator knowing only that the forcing function is as given? Can someone put me on to a systematic way to do this?

[Fred_Kohlhepp]

There is a way to estimate damping from measured data, the "log decrement" method.

I've got a sheet somewhere . . .

[JohnRudnicki]

Somewhere in the cobwebs of my mind, this rings a bell. If you manage to turn up a sheet that would be great!

[Fred_Kohlhepp · Accepted solution]

Can't find the one I built before.

Here's one from your example

[JohnRudnicki]

Thanks. Your worksheet was an education.