Storing values in a matrix

I am using the ode45 function to solve a linearized and nonlinearized vibration equation. I need to plot both of them on the same graph. The only difference between the linearized and nonlinearized is a sin function.

In order to plot the two diagrams, my professor told me that I need to first save the solved differential equations in my main file, saved in two different matricies, say x and y. And then plot them using plot(t, x, t, y).

I do not know how to save them in matricies in order to make this work. I also only have the first ODE shown because I do not know how to incorporate a second one into the mix. Any help you could give would be greatly appreciated!!!

(The second ODE has the following form: [theta(2);

-(wn^2)*(theta(1))];

function thetadot = Vib(t,theta)

m=15;

l=2;

g=9.81;

d=l/2;

Io=(1/3)*m*(l^2);

wn=sqrt((m*g*d)/Io);

thetadot = [theta(2);

-(wn^2)*sin(theta(1))];

end

------------------------------------------------------------------

m=15;

l=2;

g=9.81;

d=l/2;

Io=(1/3)*m*(l^2);

wn=sqrt((m*g*d)/Io);

theta0=5;

thetadot0=0;

t=[0:0.01:10];

[t,theta]=ode45(@Vib,t,[theta0 thetadot0]);

figure (1);

plot(t,theta(:,1));

Answer 1

[Stephan]

% Constants
m=15;
l=2;
g=9.81;
d=l/2;
Io=(1/3)*m*(l^2);
wn=sqrt((m*g*d)/Io);

% function handle for linearized ode
Vib_lin = @(~,theta,wn) [theta(2); -(wn^2).*(theta(1))];
% function handle for nonlinearized ode
Vib_nonlin = @(~,theta,wn) [theta(2); -(wn^2).*sin(theta(1))];

% input data for ode45
theta0=5;
thetadot0=0;
t=[0 10];

% solve linearized part
[t_lin,theta_lin]=ode45(@(~,theta)Vib_lin(t,theta,wn),t,[theta0 thetadot0]);
% solve nonlinearized part
[t_nonlin,theta_nonlin]=ode45(@(~,theta)Vib_nonlin(t,theta,wn),t,[theta0 thetadot0]); 

% plot results
figure (1);
plot(t_lin,theta_lin(:,1),t_nonlin,theta_nonlin(:,1));