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Solve complex eigenvalue problem?

Posted 7 months ago
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I need to find damped natural frequencies and mode shapes of a 2 DOF system in Mathematica. enter image description here

I am relatively new in Mathematica and I don't seem to find out how to solve this problem for natural frequencies ω and mode shape vectors x using Mathematica.

Thanks for your answers.

Alex

POSTED BY: Alex F
Answer
2 Replies

I think you need a differential equation.

Posted 7 months ago

The equation should hold for arbitrary x, therefore the terms in the bracket has to be zero

sol= Flatten[Solve[(- \[Omega]^2 m + I \[Omega] c + k) == 0, \[Omega]]]

The solutions provides two expressions for omega which in general are a complex.

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