If I have 3 masses displayed along a ring connected by springs, the frequencies I found were: $$\omega^2=\frac{3k}{m},0$$
I don´t understand why I have 2 double eigenfrequencies.
Is this possible, if so, what is the physical interpretation?
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If a normal frequency has more than one normal mode associated with it, then that frequency is said to be degenerate.
The total number of normal modes is always equal to $n$, the number of degrees of freedom of the system.
That explains the reason for degeneracy. Further, the notion of degeneracy is important in quantum mechanics, where normal frequencies correspond to the energies of stationary states. An unperturbed atom may have an energy level $E$ that is(say) five-fold degenerate. When the atom is perturbed (by a magnetic field, for example) the energies of five states may be changed by differing amounts so that the energy level is 'split' into five nearly equal levels. This is an important effect in the theory of atomic spectra.
