Normal mode

Summary

A normal mode of a vibrating linear system is a motion in which all parts oscillate with one frequency and a fixed phase relation. The relative amplitudes of the parts stay fixed. For the equations $M \ddot x + K x = 0$ of small oscillations, the normal modes come from the solutions of $K v = \omega^2 M v$. Their frequencies $\omega$ are the natural frequencies of the system. Every free vibration is a superposition of normal modes, which is the basis of modal analysis. The idea extends to continuous systems such as strings and membranes, where the modes are standing waves. See the definition.