Normal mode

Lore & Background

In the wave theory of physics and engineering, a mode in a dynamical system is a standing wave state of excitation, where all components are affected sinusoidally at a fixed frequency. Because no real system perfectly fits the standing wave framework, the mode concept is taken as a general characterization of specific states of oscillation, treating the system linearly so that superposition of states can be performed. Typical examples include a vibrating rope in a mechanical system, a single sound pitch in an acoustic system, a tall building oscillating under its most flexural axis in a structural system, and a resonant cavity in an electrical system.

Reader's Guide

The concept of normal modes is significant because it provides a framework for analyzing complex dynamical systems by decomposing their motion into independent, orthogonal components. Each mode has a fixed frequency and shape, and the most general motion of a linear system is a superposition of its normal modes. This independence means that excitation of one mode never causes excitation of another. The modes are numbered according to the number of half waves in the vibration, and in multi-dimensional systems each dimension is given a mode number.

Nodes—points or lines where displacement is always zero—characterize the mode shapes. The concept finds application in optics, quantum mechanics, atmospheric dynamics, and molecular dynamics. In music, normal modes of vibrating instruments are called overtones. The normal or dominant mode of a system is the one storing the minimum amount of energy for a given amplitude of the modal variable.