# Oscillation

*For other uses, see oscillator (disambiguation)*

**Oscillation** is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes is used to be synonymous with "oscillation." Oscillations occur not only in physical systems but also in biological systems and in human society.

## Simplicity

The simplest mechanical oscillating system is a mass attached to a linear spring, subject to no other forces; except for the point of equilibrium, this system is equivalent to the same one subject to a constant force such as gravity. Such a system may be approximated on an air table or ice surface. The system is in an equilibrium state when the spring is unstretched. 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 mass back to the equilibrium position, it has acquired momentum which keeps it moving beyond that position, establishing a new restoring force in the opposite sense. The time taken for an oscillation to occur is often referred to as the oscillatory *period*.

The specific dynamics of this spring-mass system are described mathematically by the simple harmonic oscillator and the regular periodic motion is known as *simple harmonic motion*. In the spring-mass system, oscillations occur because, at the static equilibrium displacement, the mass has kinetic energy which is converted into potential energy stored in the spring at the extremes of its path. The spring-mass system illustrates some common features of oscillation, namely the existence of an equilibrium and the presence of a restoring force which grows stronger the further the system deviates from equilibrium.

The harmonic oscillator offers a model of many more complicated types of oscillation and can be extended by the use of Fourier analysis.

## Damped, driven and self-induced oscillations

In real-world systems, the second law of thermodynamics dictates that there is some continual and inevitable conversion of energy into the thermal energy of the environment. Thus, *damped* oscillations tend to decay with time unless there is some net source of energy in the system. The simplest description of this decay process can be illustrated by the harmonic oscillator. In addition, an oscillating system may be subject to some external force (often sinusoidal), as when an AC circuit is connected to an outside power source. 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. For example, the phenomenon of flutter in aerodynamics occurs when an arbitrarily small displacement of an aircraft wing (from its equilibrium) results in an increase in the angle of attack of the wing on the air flow and a consequential increase in lift coefficient, leading to a still greater displacement. At sufficiently large displacements, the stiffness of the wing dominates to provide the restoring force that enables an oscillation.

## Coupled oscillations

The harmonic oscillators and the systems it models have a single degree of freedom. More complicated systems have more degrees of freedom, for example two masses and three springs (each mass being attached to fixed points and to each other). In such cases, the behavior of each variable influences that of the others. This leads to a *coupling* of the oscillations of the individual degrees of freedom. For example, two pendulum clocks mounted on a common wall will tend to synchronise. The apparent motions of the individual oscillations typically appears very complicated but a more economic, computationally simpler and conceptually deeper description is given by resolving the motion into normal modes.

## Continuous systems - waves

As the number of degrees of freedom becomes arbitrarily large, a system approaches continuity; examples include a string or the surface of a body of water. Such systems have (in the classical limit) an infinite number of normal modes and their oscillations occur in the form of waves that can characteristically propagate.

## Examples

See also: list of wave topics

### Mechanical

- Double pendulum
- Foucault pendulum
- Helmholtz resonator
- Playground swing
- String instruments
- Tuning fork
- Vibrating string
- Oscillations in the Sun (helioseismology) and stars (asteroseismology)

### Electrical

- Alternating current
- Armstrong oscillator
- Astable multivibrator
- Blocking oscillator
- Clapp oscillator
- Colpitts oscillator
- Electronic oscillator
- Hartley oscillator
- Oscillistor
- Pierce oscillator
- Relaxation oscillator
- RLC circuit
- Royer oscillator
- Vačkář oscillator
- Wien bridge oscillator
- Oscillators and Multivibrators
- Virtual Cathode Oscillator

### Electro-mechanical

### Optical

- Laser (oscillation of electromagnetic field with frequency of order
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): 10^{15}**Hz) - Oscillator Toda or self-pulsation (pulsation of output power of laser at frequencies
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): 10^{4}**Hz --**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): 10^{6}**Hz in the transient regime) - Quantum oscillator may refer to an optical local oscillator, as well as to a usual model in quantum optics.

### Biological

### Human

### Economic and social

- Business cycle
- Generation gap
- Malthusian economics
- News cycle

### Climate and geophysics

### Chemical

## See also

- BIBO stability
- Critical speed
- Dynamical system
- Feedback
- How do We Create Sinusoidal Oscillations? from Circuit Idea reveals the philosophy of LC oscillations
- Oscillation (mathematics)
- Periodic function
- Reciprocation
- Rhythm
- Self oscillation
- Signal generator
- Strange attractor
- Structural stability
- Time period
- Tuned mass damper
- Vibration
- Vibrator

## External links

- Vibrations - a chapter from an online textbook
- Dealing Vibration at work

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