Solving system of 2nd order coupled differential equation
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Hi!
I'm trying to solve a system of 2nd order coupled differential equations with matlab, but I don't know if it is possible for the problem that I have. I've looked into similar threads, but the ones I've found aren't helping a lot because they deal with much simpler problems.
The problem is the model of a two degree of freedom oscillator, where each degree of freedom interferes the accelaration, damping and stiffness of the other one.
I have to solve the following system of equations:
m(1,1)*x''(1) + m(1,2)*x''(2) + b(1,1)*x'(1) + b(1,2)*x'(2) + c(1,1)*x(1) + c(1,2)*x(2) = F(1) cos (w*t+alpha(1))
m(2,1)*x''(1) + m(2,2)*x''(2) + b(2,1)*x'(1) + b(2,2)*x'(2) + c(2,1)*x(1) + c(2,2)*x(2) = F(2) cos (w*t+alpha(2))
or, in matrix form
M*X'' + B*X' + C*X = F*cos(wt+Alpha)
Can anyone help me?
Thanks!
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Answers (1)
Roger Stafford
on 5 Jun 2013
Apply the inverse of M to your equations to get two new equations:
N = inv(M);
N*M*X" = eye(2)*X" = -N*B*X'-N*C*X+N*(F*cos(wt+Alpha))
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