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The formulation of the coupled mode theory is based on the development of the solution to an electromagnetic problem into modes. Most of the time it is eigenmodes which are taken in order to form a complete base. The choice of the basis and the adoption of certain hypothesis like parabolic approximation differs from formulation to formulation.
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
Vibration (from Latin vibrāre 'to shake') is a mechanical phenomenon whereby oscillations occur about an equilibrium point.Vibration may be deterministic if the oscillations can be characterised precisely (e.g. the periodic motion of a pendulum), or random if the oscillations can only be analysed statistically (e.g. the movement of a tire on a gravel road).
Vibration, standing waves in a string. The fundamental and the first 5 overtones in the harmonic series. A vibration in a string is a wave. Resonance causes a vibrating string to produce a sound with constant frequency, i.e. constant pitch. If the length or tension of the string is correctly adjusted, the sound produced is a musical tone.
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency.The frequency representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded domains, especially periodic functions on finite intervals.
Natural frequency, measured in terms of eigenfrequency, is the rate at which an oscillatory system tends to oscillate in the absence of disturbance. A foundational example pertains to simple harmonic oscillators, such as an idealized spring with no energy loss wherein the system exhibits constant-amplitude oscillations with a constant frequency.
Sympathetic resonance or sympathetic vibration is a harmonic phenomenon wherein a passive string or vibratory body responds to external vibrations to which it has a harmonic likeness. [1] The classic example is demonstrated with two similarly-tuned tuning forks. When one fork is struck and held near the other, vibrations are induced in the ...
Modal impact hammer with interchangeable tips and accompanying temporal and frequency responses. An ideal impact to a structure is a perfect impulse, which has an infinitely small duration, causing a constant amplitude in the frequency domain; this would result in all modes of vibration being excited with equal energy.