Damped Harmonic Oscillator fitting for data set

Hello, I am working on a Avdanced Lab fit of a damped harmonic oscilator. I am trying to use this code from the forum but I can not seem to get it to work. The code I am using is attached. The x data is time in seconds and the y data is the position.

Here is what the plot is coming out as.

Thank you so much,

Sofia

Answer 1

[Sam Chak]

Hi @Sofia Stepanoff

I think it pretty much depends on the custom nonlinear model that you supply to the fit() algorithm, as well as the lower and upper boundaries of the coefficients.

This may not the best fitted curve, but at least it shows something.

fo = fitoptions('Method', 'NonlinearLeastSquares', ...
               'Lower', [0, 0, 0, 0, 0, 91], ...
               'Upper', [10, 1, 0.01, 0.1, 0.001, 94], ...
               'StartPoint', [5 0.5 0.005 0.05 0.0005 92.5]);

ft = fittype('d - a1*exp(-b1*x)*cos(b2*x) - a2*exp(-b1*x)*sin(b2*x) + c*x', 'options', fo);

[curve, gof] = fit(x, y, ft)

curve =

General model:

curve(x) = d - a1*exp(-b1*x)*cos(b2*x) - a2*exp(-b1*x)*sin(b2*x) + c*x

Coefficients (with 95% confidence bounds):

a1 = 3.629 (3.57, 3.688)

a2 = 0.481 (0.4195, 0.5426)

b1 = 0.001029 (0.0009959, 0.001063)

b2 = 0.022 (0.02197, 0.02204)

c = 0.0002824 (0.0002621, 0.0003027)

d = 92.47 (92.44, 92.5)

gof =

struct with fields:

sse: 4.5976

rsquare: 0.9919

dfe: 255

adjrsquare: 0.9918

rmse: 0.1343

Result: