how to solve this second differential equation mx"+cx'+kx​+kx^3=f0co​s(wt)(I am stuck)

What is wrong in my code?

function Xdot=num_for(t,X)
m=100; k=1000; c=160;
ze=c/(2*sqrt(k*m));
wn=sqrt(k/m);
w=5; F=160; f=F/m;
y0=[0.01;0.1];
y1=y0.^2;
f=[0; f*cos(w*t)];
A=[0 1;-wn*wn-k/m*y1 -2*ze*wn];
Xdot=A*X+f;
end

Tspan=[0 10];
y0=[0.01;0.1];
[t,y]=ode45(@num_for,Tspan,y0);
figure
plot(t,y(:,1))

Answer 1

[Sam Chak]

Hi @seoung gi Sin

I have fixed the state matrix A and remove the unnecessary parameters. Now it should work properly.

Dynamics:

State-space model:

function Xdot = num_for(t, X)

Xdot = zeros(2,1);

m = 100;

k = 1000;

c = 160;

w = 5;

f = 160;

F = [0; (f/m)*cos(w*t)]; % input force vector

A = [0 1; -k/m -c/m]; % state matrix

Xdot = A*X + F; % state-space model

end

Run the solver:

Tspan  = [0 10];
y0     = [0.01; 0.1];
[t, y] = ode45(@num_for, Tspan, y0);
figure
plot(t, y(:,1), 'linewidth', 1.5)
grid on
xlabel('Time, t [sec]')
ylabel({'$x_{1}$'}, 'Interpreter', 'latex')
title('Time response of the 1st system state')

Result: