Solve complex eigenvalue problem?

[af9293 (Alex F)]

I need to find damped natural frequencies and mode shapes of a 2 DOF system in Mathematica.

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

[fkampas (Frank Kampas)]

I think you need a differential equation.

[mhelmle (Michael Helmle)]

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.