Editing Resonance (section)

==Universal resonance curve==
[[File:Universal Resonance Curve.svg|thumb|upright=1.3|"Universal Resonance Curve", a symmetric approximation to the normalized response of a resonant circuit; [[abscissa]] values are deviation from center frequency, in units of center frequency divided by 2Q; [[ordinate]] is relative amplitude, and phase in cycles; dashed curves compare the range of responses of real two-pole circuits for a ''Q'' value of 5; for higher ''Q'' values, there is less deviation from the universal curve. Crosses mark the edges of the 3&nbsp;dB bandwidth (gain 0.707, phase shift 45° or 0.125 cycle).]]

The exact response of a resonance, especially for frequencies far from the resonant frequency, depends on the details of the physical system, and is usually not exactly symmetric about the resonant frequency, as illustrated for the [[simple harmonic oscillator]] above.

For a lightly damped linear oscillator with a resonance frequency <math>\omega_0</math>, the ''intensity'' of oscillations <math>I</math> when the system is driven with a driving frequency ''<math>\omega</math>'' is typically approximated by the following formula that is symmetric about the resonance frequency:{{sfn|Siegman|1986|pp=105&ndash;108}}<math display="block">I(\omega) \equiv |\chi|^2  \propto \frac{1}{(\omega - \omega_0 )^2 + \left( \frac{\Gamma}{2} \right)^2 }.</math>

Where the susceptibility <math>\chi(\omega) </math> links the amplitude of the oscillator to the driving force in frequency space:{{sfn|Aspelmeyer|Kippenberg|Marquardt|2014}}<math display="block"> x(\omega) = \chi(\omega) F(\omega) </math>

The intensity is defined as the square of the amplitude of the oscillations. This is a [[Lorentzian function]], or [[Cauchy distribution]], and this response is found in many physical situations involving resonant systems. {{math|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 [[Proportionality (mathematics)|inversely proportional]] to the ''Q'' factor, which is a measure of the sharpness of the resonance.

In [[radio engineering]] and [[electronics engineering]], this approximate symmetric response is known as the ''universal resonance curve'', a concept introduced by [[Frederick E. Terman]] in 1932 to simplify the approximate analysis of radio circuits with a range of center frequencies and ''Q'' values.{{sfn|Terman|1932|p=}}{{sfn|Siebert|1986|p=113}}