Fit Underdamped oscillator to data

I have been trying to fit a under-damped oscillator equation to some data that I have. I have tried most of the online examples I can find with little success. My data can be visualized below and I have attached a file with the raw data as well.

Answer 1

[Star Strider]

This is not perfect but the best I can do:

D = load('matheu Broom rate0.2.mat');
t = D.t;
x = D.x;

[xu,ixu] = max(x);
[xl,ixl] = min(x);
xr = (xu-xl);                                                                   % Range of ‘x’
xm = mean(x);                                                                   % Estimate d-c offset
xz = x - xm;                                                                    % Subtract d-c Offset
zt = t(xz .* circshift(xz,[-1 0]) <= 0);                                        % Find zero-crossings
per = 2*mean(diff(zt));                                                         % Estimate period

objfcn = @(b,x)  b(1).*exp(b(2).*x).*(sin(2*pi*x./b(3) + 2*pi/b(4))) + b(5);    % Function to fit
ssecf = @(b) sum((objfcn(b,t) - x).^2);                                         % Sum-Of-Squares cost function
init_est = [xr; -0.01;  per;  t(ixl)/per;  xm];                                 % Initial Parameter Estimates
[s,sse] = fminsearch(ssecf, init_est)                                           % Minimise Sum-Of-Squares

tp = linspace(min(t),max(t), 250);

figure(1)
plot(t,x,'b',  tp,objfcn(s,tp), 'r')
grid
axis([xlim    0.3  0.7])
text(0.006, 0.62, sprintf('x(t) = %.3f\\cdote^{%.3f\\cdott}\\cdotsin(2\\pit\\cdot%.3f + %.3f) + %.3f', s(1:2), 1/s(3), 2*pi/s(4), s(5)))

[matheu Broom]

WOW thank you so much I was pulling my hair out over this problem. This will help me so much :)

[Star Strider]

My pleasure!

If it solved your problem, please Accept my Answer