MATLAB Answers

How can I solve for coupled differential equations?

1 view (last 30 days)
onamaewa
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:

  0 Comments

Sign in to comment.

Answers (2)

Sulaymon Eshkabilov
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

  0 Comments

Sign in to comment.


Sulaymon Eshkabilov
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

Show 2 older comments
onamaewa
onamaewa on 31 May 2019
How so? What information are you missing?
Sulaymon Eshkabilov
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.
onamaewa
onamaewa on 31 May 2019
Sorry, I forgot to add that: F = 5 * (1i * 2 * pi * FREQ)

Sign in to comment.

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by