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A normal mode of an oscillating 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 the 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. When relating to music, normal modes of vibrating instruments (strings, air pipes, drums, etc.) are called "harmonics" or "overtones". The most general motion of a system is a superposition of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other. The concept of normal modes also finds application in wave theory, optics, quantum mechanics, and molecular dynamics. ==Mode numbers== A mode of vibration is characterized by a modal frequency and a mode shape. It is numbered according to the number of half waves in the vibration. For example, if a vibrating beam with both ends pinned displayed a mode shape of half of a sine wave (one peak on the vibrating beam) it would be vibrating in mode 1. If it had a full sine wave (one peak and one trough) it would be vibrating in mode 2. In a system with two or more dimensions, such as the pictured disk, each dimension is given a mode number. Using polar coordinates, we have a radial coordinate and an angular coordinate. If you measured from the center outward along the radial coordinate you would encounter a full wave, so the mode number in the radial direction is 2. The other direction is trickier, because only half of the disk is considered due to the antisymmetric (also called skew-symmetry) nature of a disk's vibration in the angular direction. Thus, measuring 180° along the angular direction you would encounter a half wave, so the mode number in the angular direction is 1. So the mode number of the system is 2-1 or 1-2, depending on which coordinate is considered the "first" and which is considered the "second" coordinate (so it is important to always indicate which mode number matches with each coordinate direction). In linear systems each mode is entirely independent of all other modes. In general all modes have different frequencies (with lower modes having lower frequencies) and different mode shapes. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「normal mode」の詳細全文を読む スポンサード リンク
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