Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The term vibration is used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current power, the simplest mechanical oscillating system is a weight attached to a linear spring subject to only weight and tension. Such a system may be approximated on an air table or ice surface, the system is in an equilibrium state when the spring is static. If the system is displaced from the equilibrium, there is a net restoring force on the mass, tending to bring it back to equilibrium. However, in moving the back to the equilibrium position, it has acquired momentum which keeps it moving beyond that position. If a constant force such as gravity is added to the system, the time taken for an oscillation to occur is often referred to as the oscillatory period. All real-world oscillator systems are thermodynamically irreversible and this means there are dissipative processes such as friction or electrical resistance which continually convert some of the energy stored in the oscillator into heat in the environment. Thus, oscillations tend to decay with time there is some net source of energy into the system. The simplest description of this process can be illustrated by oscillation decay of the harmonic oscillator. In addition, a system may be subject to some external force. In this case the oscillation is said to be driven, some systems can be excited by energy transfer from the environment. This transfer typically occurs where systems are embedded in some fluid flow, at sufficiently large displacements, the stiffness of the wing dominates to provide the restoring force that enables an oscillation. The harmonic oscillator and the systems it models have a degree of freedom. More complicated systems have more degrees of freedom, for two masses and three springs. In such cases, the behavior of each variable influences that of the others and this leads to a coupling of the oscillations of the individual degrees of freedom. For example, two pendulum clocks mounted on a wall will tend to synchronise. This phenomenon was first observed by Christiaan Huygens in 1665, more special cases are the coupled oscillators where energy alternates between two forms of oscillation
Experimental Setup of Huygens synchronization of two clocks
Oscillation of a sequence (shown in blue) is the difference between the limit superior and limit inferior of the sequence.