How can I solve for coupled differential equations?

1 view (last 30 days)
onamaewa on 16 May 2019
Edited: Sulaymon Eshkabilov on 31 May 2019
How can I solve for the 's in the system of differential equations?
I have:
m1 = 12; m2 = 24; K1 = 6000; K2 = 3450; B1 = 40; B2 = 28; F = 5;
My equations are:

Sulaymon Eshkabilov on 31 May 2019
Edited: Sulaymon Eshkabilov on 31 May 2019
if FREQ = 0 ... 1000 Hz. Then you will have 1001 solutions with a freq step of 1 Hz.
e.g.
f = 0:1000;
F = 5* 5 * (1i * 2 * pi * f);
for ii =1:numel(F)
ICs = [0; 0; 0; 0]; % Initial Conditions
ODE=@(t,x)([x(2); (1/m1)*(F(ii)-B1*x(2)+B1*x(4)+K1*x(3)); x(4);...
(1/m2)*(-(B1+B2)*x(4)+B1*x(2)-(K1+K2)*x(3)+K1*x(1))]);
[t, x]=ode45(ODE, ts, ICs, []);
plot(t, x(:,1), 'b', t, x(:,2), 'r', t, x(:,3), 'g', t, x(:,4), 'k'), hold on
end
Good luck

Sulaymon Eshkabilov on 16 May 2019
Hi Brandon,
An easy and fast way of solving this coupled system is to use ODEx (ode23, ode45, ode113, etc) solvers. Here is one of the quick solution scripts:
m1 = 12; m2 = 24; K1 = 6000; K2 = 3450; B1 = 40; B2 = 28; F = 5;
ODE=@(t,x)([x(2); (1/m1)*(F-B1*x(2)+B1*x(4)+K1*x(3)); x(4);...
(1/m2)*(-(B1+B2)*x(4)+B1*x(2)-(K1+K2)*x(3)+K1*x(1))]);
ts = [0, 1]; % Time space
ICs = [0; 0; 0; 0]; % Initial Conditions
[t, x]=ode45(ODE, ts, ICs, []);
plot(t, x(:,1), 'b', t, x(:,2), 'r', t, x(:,3), 'g', t, x(:,4), 'k')
onamaewa on 31 May 2019
Sorry, I forgot to add that: F = 5 * (1i * 2 * pi * FREQ)