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Mode of vibration .

      What is meant by modes of vibration? Can anyone explain the ...

                In physics and engineering, for a dynamical system according wave theory, a mode is a standing wave state of excitation, in which all the components of the system will be affected sinusoidally under a specified fixed frequency. 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 where linear superposition of states can be performed. As classical examples, there are: 

* 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 systems, 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 systems, 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 systems, 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 "harmonics" or "overtones". 

* The concept of normal modes also finds application in optics, quantum mechanics, and molecular dynamics. Most dynamical system can be excited under several modes. Each mode is characterized by one or several frequencies, according the modal variable field. For example, a vibrating rope in the 2D space is defined by a single-frequency (1D axial displacement), but a vibrating rope in the 3D space is defined by two frequencies -2D axial displacement-. For a given amplitude on the modal variable, each mode will store an specific amount of energy, because of the sinusoidal excitation. From all the modes of a dynamical system, the normal or dominant mode of a system, 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, will be the mode imposing the maximum amplitude of the modal variable

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