Degeneracy of normal modes

Distinct linearly independent normal modes are degenerate if they have the same eigenfrequency. For $K\mathbf{u}={\omega }^{2}M\mathbf{u}$, 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.