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How can I solve for coupled differential equations?

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onamaewa
onamaewa 2019-5-16
关闭： MATLAB Answer Bot 2021-8-20
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:

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回答（2 个）

Sulaymon Eshkabilov
编辑：Sulaymon Eshkabilov 2019-5-31
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
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')
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Sulaymon Eshkabilov
Sulaymon Eshkabilov 2019-5-31
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.
onamaewa
onamaewa 2019-5-31
编辑：onamaewa 2019-5-31
Sorry, I forgot to add that: F = 5 * (1i * 2 * pi * FREQ)

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