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.
I think you need a differential equation.
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.