Solving a complex system of differential equations

I have a this differential equation system: , where F is a function of time (t). But I am not sure whats the easiest way to solve it in MATLAB. Lets say for example:

M = [1,0.8;0.8,7]

K = [5,0;0,10]

D = [0.15,0;0,0.35]

F = [5*exp(i*5*t); 3.65*exp(i*5*t)]

q = [X; Y]

And we want to solve for q, which is X and Y.

Answer 1

[Torsten]

%q(1) = X, q(2) = Y, q(3) = Xdot, q(4) = Ydot
M = [1,0.8;0.8,7];
K = [5,0;0,10];
D = [0.15,0;0,0.35];
F = @(t)[5*exp(i*5*t); 3.65*exp(i*5*t)] ;
tspan = [0 1];
q0 = [0 1 1 0].';
fun = @(t,q)[[q(3);q(4)];inv(M)*(F(t)-(1i*D+K)*[q(1);q(2)])];
[T,Q] = ode45(fun,tspan,q0);
figure(1)
hold on
plot(T,real(Q(:,1)))
plot(T,imag(Q(:,1)))
hold off

figure(2)
hold on
plot(T,real(Q(:,2)))
plot(T,imag(Q(:,2)))
hold off

[Ali Almakhmari]

Is the first plot for q(1) and q(2) or is it for q(3) and q(4)? Because the definition of fun makes me think its q(3) and q(4)

[Torsten]

The first plot is for the real and imaginary part of q(1) = X, the second plot is for the real and imaginary part of q(2) = Y.

q(3) and q(4) are Xdot and Ydot, respectively (as written in the headline of the code).