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How can I solve for coupled differential equations?
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How can I solve for the
's in the system of differential equations?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/219856/image.png)
I have:
m1 = 12; m2 = 24; K1 = 6000; K2 = 3450; B1 = 40; B2 = 28; F = 5;
My equations are:
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Answers (2)
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
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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')
5 Comments
Sulaymon Eshkabilov
on 31 May 2019
You said frequency 0 .. 1000 Hz that is for your external excitation force F? Let's say F = 10sin(f*t), where f is your frequency. Is that what you mean or what? ... Math is needed.
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