Damping and frequency from simulation data

I have some simulation data, for example y in the attachment. I can manually calculate the damping and frequency with logarithmic decrement, but can I do this automated? I can't seem to figure out how.

And/or can I fit a nonlinear function through my datapoints? I tried polyfit but that doesn't work with time series.

[Ameer Hamza]

How do you manually calculate the damping and frequency? Is there a mathematical formula? What type of nonlinear fit do you want to fit your data?

[MM]

I calculated it like they did here:

https://www.brown.edu/Departments/Engineering/Courses/En4/Notes/vibrations_free_damped/vibrations_free_damped.htm

With damping:

And frequency:

What type of nonlinear fit? I don't know, any that will work. I was hoping a fit would maybe let me help to calculate the frequency and daming ratio

Answer 1

[Ameer Hamza]

The following code automatically estimate the parameters from the signal.

load('PositionY_example.mat');

[val, locs] = findpeaks(y.Data);
peak_times = y.Time(locs);

t0 = t(locs(1));
tn = t(locs(2:end));
omega = mean((1:numel(tn))'./(tn-t0));

xt0 = val(1);
xtn = val(2:end);
delta = mean(log(xtn./xt0)./(1:numel(xtn))');
zeta = delta/sqrt(4*pi^2+delta^2);

As you already know the value of ω, δ, and ζ of your signal, you can calculate the nonlinear fit for your data using this equation.

[Maitham Alabbad]

What is variable t represent ?

t0 = t(locs(1));

tn = t(locs(2:end));

[MD Riaz Pervez]

t represent time. Here use t=Time therefore change that to make a single