Question

What coupling means?

Answer 1

Hint: A connection between two oscillating systems, such as pendulums connected by a spring, is referred to as coupling in classical mechanics. Both items' oscillatory patterns are impacted by the link. Two particles are said to be linked in particle physics if they are held together by one of the four fundamental forces.

Complete answer:
Wave Mechanics: Coupled harmonic oscillator
Two waves are considered to be "coupled" if they can exchange energy with one another. When the waves have a common component, this usually happens. This is illustrated with two pendulums joined by a spring. The pendulums' equations of motion are provided if they are identical.
$m{x}'=-mg\dfrac{x}{{{l}_{1}}}-k(x-y)$
$m{y}'=-mg\dfrac{y}{{{l}_{2}}}+k(x-y)$

Circuits using LC coupling
Charge oscillates in LC circuits between the capacitor and the inductor; as a result, the circuit can be described as a straightforward harmonic oscillator. The circuits are considered to be related when the magnetic flux from one inductor has the ability to influence the inductance of an inductor in an unconnected LC circuit. The equation for the coefficient of coupling, k, which describes how tightly the two circuits are coupled
$\dfrac{M}{\sqrt{{{L}_{P}}{{L}_{S}}}}=k$
where $L_p$ and $L_s$ are the inductances of the primary and secondary circuits, respectively, and M is the mutual inductance of the circuits. If every line in the secondary inductor is threaded by the flux lines of the primary inductor, then the coefficient of coupling is 1 and $M=\sqrt{{{L}_{P}}{{L}_{S}}}$. The majority of systems, however, are not completely linked since leakage occurs frequently in real life.

Note: A coupling is a mechanical component used to join two shafts at their ends. A coupling's main function is to connect two spinning pieces of machinery while allowing for end movements and a minimal amount of misalignment. The connection enables the transfer of power.