Resonance

:This article is about resonance in physics. For other senses of this term, see resonance (disambiguation).

Theory

For an oscillator with a resonant frequency Ω, the intensity of oscillations I when the system is driven with a driving frequency ω is given by:

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:I(omega) propto rac{rac{Gamma}{2}}{(omega - Omega)^2 + left( rac{Gamma}{2} ight)^2 }.

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The intensity is defined as the square of the amplitude of the oscillations. This is a Lorentzian function, and this response is found in many physical situations involving resonant systems. Γ is a parameter dependent on the damping of the oscillator, and is known as the linewidth of the resonance. Heavily damped oscillators tend to have broad linewidths, and respond to a wider range of driving frequencies around the resonant frequency. The linewidth is inversely proportional to the Q factor, which is a measure of the sharpness of the resonance.

Related Topics:
Lorentzian function - Damping - Q factor

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