Why my ODE is not solving?

I'm trying to solve the ODE with an input of a cosine wave (x1) but i am not getting the output in a wave form. Please help me out. Thanks!

function [] = call_spring()
t=0:0.001:10;
y0=[0,1]; 
x1=2.5*cos(4*pi*t);
[t,y]=ode45(@spring,t,y0);
plot(t,y,t,x1)
    function dzdt = spring(t,y)
        k=342; m=2.853; x1=2.5*cos(4*pi*t);
        y1=y(1); 
        y2=y(2); 
        dzdt = [y2 ; (-k/m)*(x1-y1)];
    end
end

Answer 1

[Sam Chak]

Hi @Aung Moe Zaw

Because of the sign in this line. (minus) (minus) = plus. It means that energy is continuously injected into the system, and destabilizes it.

(-k/m)*(x1 - y1)

function [] = call_spring()

t = 0:0.001:10;

y0 = [0, 1];

x1 = 2.5*cos(4*pi*t);

[t, y] = ode45(@spring, t, y0);

plot(t, y, t, x1)

end

function dzdt = spring(t, y)

k = 342;

m = 2.853;

x1 = 2.5*cos(4*pi*t);

y1 = y(1);

y2 = y(2);

dzdt = [y2;

(-k/m)*(x1 + y1)];

end

Result

Also, please double check your equation. Could be this one too:

(-k/m)*y1 + (1/m)*x1

[Aung Moe Zaw]

Thank you

[Aung Moe Zaw]

y is plotted as orange and blue, is there a way i can just display the blue wave?

[Sam Chak]

You are welcome, @Aung Moe Zaw

There are two vectors in y. To plot only the first vector, then replace

plot(t, y, t, x1)

with

plot(t, y(:,1), t, x1)
grid on
xlabel('Time, t')
ylabel('y_{1} and x_{1}')
title('Time response of y_{1}, perturbed by x_{1}')
legend('y_{1}', 'x_{1}')

[Aung Moe Zaw]

Thank you very much!!