How to fix a syntax in the oscillator's plot code?

Hi!

My assignment would be to observe harmonic oscillator. I have created a function for the driven oscillator's equation of motion. My problem is that now my code is plotting the results of the differential equation, but I would like to plot the oscillator's place which is marked as x_2.

So it should be that the figures should plot the place of the oscillator. The oscillator is starting from the rest in the beginning.

Thus,

In the figure 1: the place of the oscillator, which is starting from the rest.

In the figure 2: the place of the oscillator with the values of the parameter ω ∈ {0.1, 1.0, 1.1}. The others parameters' valeus stay the same.

So, my question is that how could I get the place out of the function for the driven oscillator?

Here is my function for the driven oscillator:

function dx=DrivenOsc(t,x,T0,omega,M,F,omega0)

dx = [-1/T0*x(1)-omega0^2*x(2)+F/M*cos(omega*t);x(1)];

Here is my code for the plotting:

clear all

close all

T0 = 10;

omega0 = 1;

M = 1;

F = 1;

omega = 1;

t = 0;

x_1 = 0;

x_2 = 0;

x = [x_1 x_2];

t=0:0.01:10*T0;

options=[];

options=odeset(options,'RelTol',1e-7,'AbsTol',1e-7);

[tout,yout]=ode45(@DrivenOsc,t,x,options,T0,omega,M,F,omega0);

figure(1)

plot(tout,yout);

xlabel('Aika');

ylabel('Värähtelyt');

grid on

figure(2)

subplot(3,1,1)

T0 = 10;

omega0 = 1;

M = 1;

F = 1;

omega = 0.1;

t = 0;

x_1 = 0;

x_2 = 0;

x = [x_1 x_2];

t=0:0.01:10*T0;

options=[];

options=odeset(options,'RelTol',1e-7,'AbsTol',1e-7);

[tout,yout]=ode45(@DrivenOsc,t,x,options,T0,omega,M,F,omega0);

plot(tout,yout);

xlabel('Aika');

ylabel('Värähtelyt');

grid on

subplot(3,1,2)

T0 = 10;

omega0 = 1;

M = 1;

F = 1;

omega = 1.0;

t = 0;

x_1 = 0;

x_2 = 0;

x = [x_1 x_2];

t=0:0.01:10*T0;

options=[];

options=odeset(options,'RelTol',1e-7,'AbsTol',1e-7);

[tout,yout]=ode45(@DrivenOsc,t,x,options,T0,omega,M,F,omega0);

plot(tout,yout);

xlabel('Aika');

ylabel('Värähtelyt');

grid on

subplot(3,1,3)

T0 = 10;

omega0 = 1;

M = 1;

F = 1;

omega = 1.1;

t = 0;

x_1 = 0;

x_2 = 0;

x = [x_1 x_2];

t=0:0.01:10*T0;

options=[];

options=odeset(options,'RelTol',1e-7,'AbsTol',1e-7);

[tout,yout]=ode45(@DrivenOsc,t,x,options,T0,omega,M,F,omega0);

plot(tout,yout);

xlabel('Aika');

ylabel('Värähtelyt');

grid on

Thank you for your help!

Answer 1

[Alan Stevens]

Like this (both x_1 and x_2 are contained in y)

T0 = 10;
omega0 = 1;
M = 1;
F = 1;
x_1 = 0;
x_2 = 0;
x_0 = [x_1 x_2];
tspan=0:0.01:10*T0;
options=[];
options=odeset(options,'RelTol',1e-7,'AbsTol',1e-7);

 omega = [0.1, 1, 1.1];
 figure
 hold on
 for i = 1:numel(omega)

    [tout,yout]=ode45(@(t,y)DrivenOsc(t,y,T0,omega(i),M,F,omega0),tspan,x_0,options);
    subplot(3,1,i)
    plot(tout,yout);  % If you want just x_2 then plot(tout,yout(:,2))
    title(['\omega = ' num2str(omega(i))])
    xlabel('Aika');
    ylabel('Värähtelyt');
    legend('Nopeus','asema')  % Nopeus = Velocity,  asema = position according to Google translate.
    grid on

 end

function dx=DrivenOsc(t,x,T0,omega,M,F,omega0)
dx = [-1/T0*x(1)-omega0^2*x(2)+F/M*cos(omega*t);x(1)];
end

[Jenni]

Excellent, thank you so much @Alan Stevens!

P.S I truly appreciate for googling Finnish translations! :D