In physics, two objects are said to be coupled when they are interacting with each other. In classical mechanics, coupling is a connection between two oscillating systems, such as pendulums connected by a spring. The connection affects the oscillatory pattern of both objects. In particle physics, two particles are coupled if they are connected by one of the four fundamental forces. Wave mechanics Coupled harmonic oscillator If two 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. If the pendulums are identical, then their equations of motion are given by These equations represent the simple harmonic motion of the pendulum with an added coupling factor of the spring. This behavior is also seen in certain molecules (such as CO2 and H2O), wherein two of the atoms will vibrate around a central one in a similar manner. Coupled LC circuits In LC circuits, charge oscillates between the capacitor and the inductor and can therefore be modeled as a simple harmonic oscillator. When the magnetic flux from one inductor is able to affect the inductance of an inductor in an unconnected LC circuit, the circuits are said to be coupled. The coefficient of coupling k defines how closely the two circuits are coupled and is given by the equation where M is the mutual inductance of the circuits and Lp and Ls 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 In practice, however, there is often leakage, so most systems are not perfectly coupled. Chemistry Spin-spin coupling Spin-spin coupling occurs when the magnetic field of one atom affects the magnetic field of another nearby atom. This is very common in NMR imaging. If the atoms are not coupled, then there will be two individual peaks, known as a doublet, representing the individual atoms. If coupling is present, then there will be a triplet, one larger peak with two smaller ones to either side. This occurs due to the spins of the individual atoms oscillating in tandem. Astrophysics Objects in space which are coupled to each other are under the mutual influence of each other's gravity. For instance, the