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I'm studying Small Oscillations and I'm having a problem with normal modes.

In some texts, there is written that normal modes are the eigenvectors of the matrix $V- \omega^2 V$ where V is the matrix of potential energy and T is the matrix of kinetic energy.

Some of them normalize the eigenvector, other don't do it.

In other texts, there is written that normal modes are the coordinates that uncouple the equation of motion and that I can find them as ζ=$B^-1$ η where ζ is the column vector of these normal modes, η is the column vector of initial coordinates and $B^-1$ is the modal matrix (but... for the modal matrix, do I have to normalize eigenvectors?)

Which is the most correct way to find normal modes?

Thank you

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# Small oscillations: How to find normal modes?

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