Editing Normal mode (section)

=== Mode ===
In the [[Wave|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 principle|superposition]] of states can be performed.

Typical 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,{{dubious|reason=wouldn't that be a superposition of two modes?|date=April 2020}} 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.