Solving coupled second order differential equations

Hi,

I constantly get an error that I do not know how to resolve when I run this code. Any help would be greatly appreciated. The Force function applies a force of 50N @ t = 0 and equals 0 at all other time steps.

syms c k m1 m2 x1(t) x2(t) t F Y;

% 1st and 2nd derivative

dx1 = diff(x1);

d2x1 = diff(x1,2);

dx2 = diff(x2);

d2x2 = diff(x2,2);

% Defining equations

Eq1 = d2x1 == -(c/m1)*(dx1-dx2) - (k/m1)*(x1(t)-x2(t)) + F/m1;

Eq2 = d2x2 == -(c/m2)*(dx1-dx2) + (k/m2)*(x1(t)-x2(t));

[VF,subs] = odeToVectorField(Eq1, Eq2);

ftotal = matlabFunction(VF,'Vars',{t,Y,F,c,k,m1,m2});

m1 = 10;

m2 = 20;

c = 30;

k = 5;

F = @(t) Force(t);

tspan = [0 1];

ic = [8 0 0 0];

[t,Y] = ode45(@(t,Y) ftotal(t,Y,F,c,k,m1,m2), tspan, ic);

figure

plot(t, Y)

grid

legend(string(subs))

[Torsten]

The value of the "Force" function at t=0 must somehow be part of the initial conditions ic.

As part of the differential equations, it won't influence the result.

Answer 1

[Alan Stevens]

Something like this?

m1 = 10;
m2 = 20;
c  = 30;
k  = 5;
tspan = [0 1];                                             
ic = [8 0 0 0];                                             
[t,Y] = ode45(@(t,Y) ftotal(t,Y,c,k,m1,m2), tspan, ic);
figure
plot(t, Y)
xlabel('t'), ylabel('y and dydt')
grid
legend('y1','dy1/dt','y2','dy2dt')

function dYdt = ftotal(t,Y,c,k,m1,m2)

        y1 = Y(1);   dy1dt = Y(2);
        y2 = Y(3);   dy2dt = Y(4);
        
        dYdt = [dy1dt;
                -(c/m1)*(dy1dt - dy2dt) - (k/m1)*(y1 - y2) + 50*(t==0)/m1;
                dy2dt;
                -(c/m2)*(dy1dt - dy2dt) + (k/m2)*(y1 - y2)];

end

[Alan Stevens]

Instead of 50*(t==0)/m1; you could try 50*(t<0.01)/m1; but you still won't see an effect. However, if you try 5000*(t<0.01)/m1; you start to see an effect. If you try decreasing the 5000 to smaller values, towards 50, you see the effect getting smaller and smaller.