MATLAB: Convolution integral with ode45

convolutiondamped eomode45sdof

Hi guys, can someone help me solve this equation of motion using ode45 or any other way? I dont know how to approach the convolution integral. Thank you!

Best Answer

Try this: 
odefcn = @(t,y,c,F,k,m,w) [y(2); -(k.*y(1) - F.*cos(t.*w) + integral(@(tau)c(t - tau).*y(2).*tau, 0, t))./m];
c = @(t) exp(-t.^2);                                                                    % Make Something Up
[F,k,m,w] = deal(rand,rand,rand,rand);                                                  % Replace With Correct Values
tspan = [0 10];
ics = [1; 1];
[t,y] = ode45(@(t,y)odefcn(t,y,c,F,k,m,w), tspan, ics);
figure
plot(t, y)
hl = legend('$u(t)$', '$\dot{u}(t)$');
set(hl,'Interpreter','latex')
Noite that ‘c’ actually has to be defined as a function in order for this to work. Supply the correct one.
I derived it with the help of the Symbolic Math Toolbox.
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