= Degeneracy of normal modes
Distinct linearly independent <normal modes> are degenerate if they have the same <eigenfrequency>. For $K\mathbf u=\omega^2M\mathbf u$, their <eigenvectors> span a common <eigenspace>; linear combinations in that space are also modes with the same <frequency>. A <symmetry> preserving both quadratic <energies> maps this space into itself. Higher-dimensional irreducible <symmetry> representations can enforce degeneracy, while perturbations breaking that <symmetry> can split it. Degeneracies can also occur accidentally without such <symmetry> protection.
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