Consider the following system consisting of 3 masses and 4 springs :
I have learned that this system posseses three normal modes, corresponding to its three natural frequencies, say $\omega_0$, $\omega_1$ and $\omega_2$.
I'm interested in the movement of the masses that each of the three normal modes represents.
I know that one normal mode correponds to the middle mass $m_2$ being fixed and the other outer masses $m_1$ and $m_3$ moving in opposite directions with the same frequency ... But what about the two other normal modes ?
For a system of 2 masses and 3 springs, I've learned that the first normal mode represents the motion of the two masses, with the same frequency and with same phase; while the second normal represents the motion of the two masses, with some other common frequency but with phase difference of ninety degrees ( one is moving in the opposite direction of the other ).
But what about a system of 3 masses and 4 springs? Or say, $N$ masses and $(N+1)$ springs ?
I've found many mathematical demonstrations (with eigenvectors and eigenvalues) of the solution of this system, representing the motion of the masses, but I can't see the physical interpretation.