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Normal mode
A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions.
The most general motion of a linear system is a superposition of its normal modes. The modes are "normal" in the sense that they move independently. An excitation of one mode will never cause excitation of a different mode. In mathematical terms, normal modes are orthogonal to each other.
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.
Typical examples include:
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 – discuss] 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.
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Normal mode
A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions.
The most general motion of a linear system is a superposition of its normal modes. The modes are "normal" in the sense that they move independently. An excitation of one mode will never cause excitation of a different mode. In mathematical terms, normal modes are orthogonal to each other.
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.
Typical examples include:
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 – discuss] 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.