MATLAB: Ode45 Set of 3 second order ODE not solving correctly

Question

Attempting to solve 3 2nd order ODE's (broken down into 6 1st orders here) using ode45. My answer does not appear to come out correctly and am not sure what I am doing wrong.

CODE:

tspan=[0 60]; %Time Boundaries

x0=[0 0 0 0 0 0]; %Inital Values of disp and vel

[t,x]=ode45(@output,tspan, x0) %Implement ode45 solver

plot(t,x)

xlabel('time')

ylabel('displacement/velocity')

title('Problem 25.18')

legend('Displacement','Velocity')

function dxdt=output(t,x) %Create system of equations

m1=60;

m2=70;

m3=80;

k1=50;

k2=100;

k3=50;

g=9.81;

dxdt=zeros(6,1);

dxdt(1)=x(1);

dxdt(2)=x(2);

dxdt(3)=x(3);

dxdt(4)=g+(k2/m1)*(x(2)-x(1))-(k1/m1)*x(1);

dxdt(5)=g+(k3/m2)*(x(3)-x(2))+(k2/m2)*(x(1)-x(2));

dxdt(6)=g+(k3/m3)*(x(2)-x(3));

end

Answer 1

Hi William,

you are close on this. x1,x2,x3 are postions and x4,x5,x6 are velocities so the appropriate lines of code are

dxdt(1)=x(4);
dxdt(2)=x(5);
dxdt(3)=x(6);

in which case you get oscillations.

g is positive which makes positive x in the direction of down. That's all right as long as you acknowledge the fact in a picture or something. g = -9.81 would put positive x up which is more common.