Finding Angular Frequency of an Oscillation

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Macaulay Wright
Macaulay Wright 2020-3-31
评论： Star Strider 2020-3-31
I have currently produced a code to plot a Van der Pol oscillator, I can calculate the period by physically looking at the graph, but I am unsure on how to do this using a MATLAB code to get a result digitally.
My main focus is to get a printed value for the angular frequency (w - omega), so my first thought was to calculate the period and then use the equation w = (2pi/T).
Please can I get some guidance on producing a small script to calculate angular frequency? (w = 1 with the current model)
I have attached the code for the oscillation below.
Thanks in advance.
% simulation parameters
DT = 0.01; % Time step
N = 10000; % number of discrete time points
% Equation parameter
mu = 0.1;
% declare array to store discrete time samples
x = zeros(1,N);
% set boundary conditions
x(1) = -0.01;
x(2) = 0.0;
% Simulate using recurrance relation
for i = 3:N
phi = mu*DT/2*(x(i-1)^2-1);
x(i) = x(i-1)*(2-DT^2)/(1+phi) - x(i-2)*(1-phi)/(1+phi);
end
% plot
plot((1:N)*DT,x,'r')
% Calculating angular frequency

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Star Strider
Star Strider 2020-3-31
Likely the easiest way would be to find the times of the positive peaks, then calculate from there:
[pks,pktimes] = findpeaks(x, (1:N)*DT);
Period = mean(diff(pktimes))
The findpeaks function requires the Signal Processing Toolbox. A similar function is islocalmax, introduced in R2017b. (There are still other ways if you have neither of these functions.)
  2 个评论
Macaulay Wright
Macaulay Wright 2020-3-31
编辑：Macaulay Wright 2020-3-31
Thank you for the quick response, that piece of code works perfectly and was just what I was trying to acheive. I will now input the angular frequency equation using the new found period value.
Thank you again.

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