Editing Coupling (physics) (section)

==Wave mechanics==

=== Coupled harmonic oscillator ===
[[File:Coupled.svg|thumb|Coupled pendulums connected by a spring]]
If two [[Waves (physics)|waves]] are able to transmit [[energy]] to each other, then these waves are said to be "coupled." This normally occurs when the waves share a common component. An example of this is two pendulums connected by a [[Spring (device)|spring]]. If the pendulums are identical, then their equations of motion are given by
<math display="block">m\ddot{x} = -mg\frac{x}{l_1} - k(x-y)</math>
<math display="block">m\ddot{y} = -mg \frac{y}{l_2} + k(x-y)</math>

These equations represent the [[simple harmonic motion]] of the pendulum with an added coupling factor of the spring.<ref name=":0">{{Cite book|title=The Physics of Vibrations and Waves | edition = Fourth | last=Pain|first=H.J.| publisher=Wiley | year=1993| isbn=0-471-93742-8|location=West Sussex, England}}</ref> This behavior is also seen in certain molecules (such as [[Carbon dioxide|CO<sub>2</sub>]] and H<sub>2</sub>O), wherein two of the atoms will vibrate around a central one in a similar manner.<ref name=":0" />

=== Coupled LC circuits ===
[[File:LC coupling.png|thumb|Two LC circuits coupled together.]]
In [[LC circuit]]s, charge oscillates between the [[capacitor]] and the [[inductor]] and can therefore be modeled as a simple harmonic oscillator. When the [[magnetic flux]] from <dfn>one inductor is able </dfn>to affect the [[inductance]] of an inductor in an unconnected LC circuit, the circuits are said to be coupled.<ref name=":0" /> The coefficient of coupling k defines how closely the <dfn>two circuits are coupled</dfn> and is given by the equation
<math display="block">\frac{M}{\sqrt{L_p L_s}} = k</math>
where M is the [[Mutual Inductance|mutual inductance]] of the circuits and L<sub>p</sub> and L<sub>s</sub> are the inductances of the primary and secondary circuits, respectively. If the flux lines of the primary inductor thread every line of the secondary one, then the coefficient of coupling is 1 and <math display="inline">M = \sqrt{L_p L_s}</math> In practice, however, there is of<dfn>ten leakage</dfn>, so most systems are not perfectly coupled.<ref name=":0" />[[File:1H NMR Ethyl Acetate Coupling shown - 2.png|thumb|Peaks in an NMR image of Ethyl Acetate.]]