In the wave theory of physics and engineering, a mode in a dynamical system is a standing wave state of excitation, in which all the components of the system will be affected sinusoidally at a fixed frequency associated with that mode.
Because no real system can perfectly fit under the standing wave framework, the mode concept is taken as a general characterization of specific states of oscillation, thus treating the dynamic system in a linear fashion, in which linear superposition of states can be performed.
Classical examples include
* In a mechanical dynamical system, a vibrating rope is the most clear example of a mode, in which the rope is the medium, the stress on the rope is the excitation, and the displacement of the rope with respect to its static state is the modal variable.
* In an acoustic dynamical system, a single sound pitch is a mode, in which the air is the medium, the sound pressure in the air is the excitation, and the displacement of the air molecules is the modal variable.
* In a structural dynamical system, a high tall building oscillating under its most flexural axis is a mode, in which all the material of the building -under the proper numerical simplifications- is the medium, the seismic/wind/environmental solicitations are the excitations and the displacements are the modal variable.
* In an electrical dynamical system, a resonant cavity made of thin metal walls, enclosing a hollow space, for a particle accelerator is a pure standing wave system, and thus an example of a mode, in which the hollow space of the cavity is the medium, the RF source (a Klystron or another RF source) is the excitation and the electromagnetic field is the modal variable.
* When relating to music, normal modes of vibrating instruments (strings, air pipes, drums, etc.) are called "overtones".
The concept of normal modes also finds application in other dynamical systems, such as optics, quantum mechanics, atmospheric dynamics and molecular dynamics.
Most dynamical systems can be excited in several modes, possibly simultaneously. Each mode is characterized by one or several frequencies, according to the modal variable field. For example, a vibrating rope in 2D space is defined by a single-frequency (1D axial displacement), but a vibrating rope in 3D space is defined by two frequencies (2D axial displacement).
For a given amplitude on the modal variable, each mode will store a specific amount of energy because of the sinusoidal excitation.
The normal or dominant mode of a system with multiple modes will be the mode storing the minimum amount of energy for a given amplitude of the modal variable, or, equivalently, for a given stored amount of energy, the dominant mode will be the mode imposing the maximum amplitude of the modal variable.