Oscillation
Overview

Oscillation is the repetitive variation, typically in time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

, of some measure about a central value (often a point of equilibrium
Mechanical equilibrium
A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....

) or between two or more different states. Familiar examples include a swinging pendulum
Pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position...

and AC
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....

power. The term vibration
Vibration
Vibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...

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
Ecology
Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...

and in human society
Society
A society, or a human society, is a group of people related to each other through persistent relations, or a large social grouping sharing the same geographical or virtual territory, subject to the same political authority and dominant cultural expectations...

.
The simplest mechanical oscillating system is a mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

attached to a linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...

spring
Spring (device)
A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication...

subject to no other forces.
Discussions
Encyclopedia
Oscillation is the repetitive variation, typically in time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

, of some measure about a central value (often a point of equilibrium
Mechanical equilibrium
A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....

) or between two or more different states. Familiar examples include a swinging pendulum
Pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position...

and AC
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....

power. The term vibration
Vibration
Vibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...

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
Ecology
Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...

and in human society
Society
A society, or a human society, is a group of people related to each other through persistent relations, or a large social grouping sharing the same geographical or virtual territory, subject to the same political authority and dominant cultural expectations...

.

Simple harmonic oscillator

The simplest mechanical oscillating system is a mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

attached to a linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...

spring
Spring (device)
A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication...

subject to no other forces. Such a system may be approximated on an air table or ice surface. The system is in an equilibrium
Mechanical equilibrium
A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....

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 mass back to the equilibrium position, it has acquired momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

which keeps it moving beyond that position, establishing a new restoring force in the opposite sense. If a constant force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

such as gravity is added to the system, the point of equilibrium is shifted. The time taken for an oscillation to occur is often referred to as the oscillatory period.

The specific dynamics
Dynamics (mechanics)
In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion...

of this spring-mass system are described mathematically by the simple harmonic oscillator and the regular periodic motion is known as simple harmonic motion
Simple harmonic motion
Simple harmonic motion can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. Additionally, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum and molecular vibration....

. In the spring-mass system, oscillations occur because, at the static
Statics
Statics is the branch of mechanics concerned with the analysis of loads on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity...

equilibrium displacement, the mass has kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

which is converted into potential energy
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

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.

Damped and driven oscillations

All real-world oscillator systems are thermodynamically irreversible. This means there are dissipative processes such as friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

or electrical resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

which continually convert some of the energy stored in the oscillator into heat in the environment. This is called damping. Thus, oscillations tend to decay with time unless there is some net source of energy into the system. The simplest description of this decay process can be illustrated by oscillation decay of the harmonic oscillator.

In addition, an oscillating system may be subject to some external force, as when an AC circuit
Electronic circuit
An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow...

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
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

flow. For example, the phenomenon of flutter in aerodynamics
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...

occurs when an arbitrarily small displacement of an aircraft
Aircraft
An aircraft is a vehicle that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines.Although...

wing
Wing
A wing is an appendage with a surface that produces lift for flight or propulsion through the atmosphere, or through another gaseous or liquid fluid...

(from its equilibrium) results in an increase in the angle of attack
Angle of attack
Angle of attack is a term used in fluid dynamics to describe the angle between a reference line on a lifting body and the vector representing the relative motion between the lifting body and the fluid through which it is moving...

of the wing on the air
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

flow and a consequential increase in lift coefficient, leading to a still greater displacement. At sufficiently large displacements, the stiffness
Stiffness
Stiffness is the resistance of an elastic body to deformation by an applied force along a given degree of freedom when a set of loading points and boundary conditions are prescribed on the elastic body.-Calculations:...

of the wing dominates to provide the restoring force that enables an oscillation.

Coupled oscillations

The harmonic oscillator and the systems it models have a single degree of freedom
Degrees of freedom (physics and chemistry)
A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...

. 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 (of identical frequency) mounted on a common wall will tend to synchronise. This phenomenon
Odd sympathy
The phrase odd sympathy appears in the record of a letter by Dutch mathematician and physicist Christiaan Huygens to Sir Robert Moray as presented to the Royal Society of London, relating to the tendency of two pendulum clocks to synchronize with opposite phases when suspended side by side...

was first observed by Christiaan Huygens in 1665. The apparent motions of the compound oscillations typically appears very complicated but a more economic, computationally simpler and conceptually deeper description is given by resolving the motion into normal mode
Normal mode
A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies...

s.

More special cases are the coupled oscillators where the energy alternates between two forms of oscillation. Well-known is the Wilberforce pendulum
Wilberforce pendulum
A Wilberforce pendulum, invented by British physicist Lionel Robert Wilberforce around 1896, consists of a mass suspended by a long helical spring and free to turn on its vertical axis, twisting the spring. It is an example of a coupled mechanical oscillator, often used as a demonstration in...

, where the oscillation alternates between an elongation of a vertical spring and the rotation of an object at the end of that spring.

Continuous systems – waves

As the number of degrees of freedom becomes arbitrarily large, a system approaches continuity
Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modelled as a continuous mass rather than as discrete particles...

; examples include a string or the surface of a body of water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

. Such systems have (in the classical limit
Classical limit
The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters. The classical limit is used with physical theories that predict non-classical behavior...

) an infinite number of normal modes and their oscillations occur in the form of wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

s that can characteristically propagate.

Mechanical

• Double pendulum
Double pendulum
In mathematics, in the area of dynamical systems, a double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. The motion of a double pendulum is governed by a set of...

• Foucault pendulum
Foucault pendulum
The Foucault pendulum , or Foucault's pendulum, named after the French physicist Léon Foucault, is a simple device conceived as an experiment to demonstrate the rotation of the Earth. While it had long been known that the Earth rotated, the introduction of the Foucault pendulum in 1851 was the...

• Helmholtz resonator
Helmholtz resonance
Helmholtz resonance is the phenomenon of air resonance in a cavity, such as when one blows across the top of an empty bottle. The name comes from a device created in the 1850s by Hermann von Helmholtz, the "Helmholtz resonator", which he, the author of the classic study of acoustic science, used to...

• Oscillations in the Sun (helioseismology
Helioseismology
Helioseismology is the study of the propagation of wave oscillations, particularly acoustic pressure waves, in the Sun. Unlike seismic waves on Earth, solar waves have practically no shear component . Solar pressure waves are believed to be generated by the turbulence in the convection zone near...

), stars (asteroseismology
Asteroseismology
Asteroseismology also known as stellar seismology is the science that studies the internal structure of pulsating stars by the interpretation of their frequency spectra. Different oscillation modes penetrate to different depths inside the star...

) and Neutron-star oscillations
Neutron-star oscillations
Asteroseismology studies the internal structure of our Sun and other stars using oscillations. These can be studied by interpreting the temporal frequency spectrum acquired through observations...

.
• Quantum harmonic oscillator
Quantum harmonic oscillator
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics...

• Playground swing
Swing (seat)
A swing is a hanging seat, usually found at playgrounds for children, a circus for acrobats, or on a porch for relaxing. The seat of a swing may be suspended from chains or ropes. Once a swing is in motion it continues to oscillate like a pendulum until external interference or drag brings it to a...

• String instrument
String instrument
A string instrument is a musical instrument that produces sound by means of vibrating strings. In the Hornbostel-Sachs scheme of musical instrument classification, used in organology, they are called chordophones...

s
• Torsional vibration
Torsional vibration
Torsional vibration is angular vibration of an object—commonly a shaft along its axis of rotation. Torsional vibration is often a concern in power transmission systems using rotating shafts or couplings where it can cause failures if not controlled....

• Tuning fork
Tuning fork
A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs formed from a U-shaped bar of elastic metal . It resonates at a specific constant pitch when set vibrating by striking it against a surface or with an object, and emits a pure musical tone after waiting a...

• Vibrating string
Vibrating string
A vibration in a string is a wave. Usually a vibrating string produces a sound whose frequency in most cases is constant. Therefore, since frequency characterizes the pitch, the sound produced is a constant note....

• Wilberforce pendulum
Wilberforce pendulum
A Wilberforce pendulum, invented by British physicist Lionel Robert Wilberforce around 1896, consists of a mass suspended by a long helical spring and free to turn on its vertical axis, twisting the spring. It is an example of a coupled mechanical oscillator, often used as a demonstration in...

• Lever escapement
Lever escapement
The lever escapement is a key component of the typical movement found in most mechanical wristwatches, pocket watches and many small mechanical non-pendulum clocks....

Electrical

• Alternating current
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....

• Armstrong (or Tickler or Meissner) oscillator
Armstrong oscillator
The Armstrong oscillator is named after its inventor, the electrical engineer Edwin Armstrong. It is sometimes called a tickler oscillator because the feedback needed to produce oscillations is provided using a tickler coil via magnetic coupling between coil L and coil T...

• Astable multivibrator
• Blocking oscillator
Blocking oscillator
A blocking oscillator is a simple configuration of discrete electronic components which can produce a free-running signal, requiring only a resistor, a transformer, and one amplifying element. The name is derived from the fact that the transistor is cut-off or "blocked" for most of the...

• Butler oscillator
• Clapp oscillator
Clapp oscillator
The Clapp oscillator is one of several types of electronic oscillator constructed from a transistor and a positive feedback network, using the combination of an inductance with a capacitor for frequency determination, thus also called LC oscillator.It was published by James Kilton Clapp in 1948...

• Colpitts oscillator
Colpitts oscillator
A Colpitts oscillator, invented in 1920 by American engineer Edwin H. Colpitts, is one of a number of designs for electronic oscillator circuits using the combination of an inductance with a capacitor for frequency determination, thus also called LC oscillator...

• Delay line oscillator
Delay line oscillator
A delay line oscillator is a form of electronic oscillator that uses a delay line as its principal timing element.The circuit is set to oscillate by inverting the output of the delay line and feeding that signal back to the input of the delay line with appropriate amplification...

• Dow (or ultra-audion) oscillator
• Electronic oscillator
Electronic oscillator
An electronic oscillator is an electronic circuit that produces a repetitive electronic signal, often a sine wave or a square wave. They are widely used in innumerable electronic devices...

• Hartley oscillator
Hartley oscillator
The Hartley oscillator is an electronic oscillator circuit that uses an inductor and a capacitor in parallel to determine the frequency. Invented in 1915 by American engineer Ralph Hartley, the distinguishing feature of the Hartley circuit is that the feedback needed for oscillation is taken from...

• Oscillistor
Oscillistor
An oscillistor is a semiconductor device, consisting of a semiconductor specimen placed in magnetic field, and a resistor after a power supply. The device produces high-frequency oscillations, which are very close to sinusoidal....

• Pierce oscillator
Pierce oscillator
The Pierce oscillator is a type of electronic oscillator particularly well-suited for use in piezoelectric crystal oscillator circuits. Named for its inventor, George W. Pierce , the Pierce oscillator is a derivative of the Colpitts oscillator...

• Relaxation oscillator
Relaxation oscillator
A relaxation oscillator is an oscillator based upon the behavior of a physical system's return to equilibrium after being disturbed. That is, a dynamical system within the oscillator continuously dissipates its internal energy...

• RLC circuit
RLC circuit
An RLC circuit is an electrical circuit consisting of a resistor, an inductor, and a capacitor, connected in series or in parallel. The RLC part of the name is due to those letters being the usual electrical symbols for resistance, inductance and capacitance respectively...

• Royer oscillator
Royer oscillator
A Royer oscillator is an electronic oscillator which has the advantages of simplicity, low component count, rectangle waveforms and easy transformer isolation. It was first described by George H...

• Vačkář oscillator
Vackár oscillator
A Vackář oscillator is a variation of the split-capacitance oscillator model. It is similar to a Colpitts oscillator or a Clapp oscillator in this respect. It differs in that the output level is relatively stable over frequency, and has a wider bandwidth when compared to a Clapp design.In 1949,...

• Wien bridge oscillator
Wien bridge oscillator
A Wien bridge oscillator is a type of electronic oscillator that generates sine waves. It can generate a large range of frequencies. The oscillator is based on a bridge circuit originally developed by Max Wien in 1891....

Optical

• Laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

(oscillation of electromagnetic field
Electromagnetic field
An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...

with frequency of order 1015 Hz)
• Oscillator Toda
Oscillator Toda
In physics, the Toda oscillator is special kind of nonlinear oscillator; it is vulgarization of the Toda field theory, which is a continuous limit of Toda's chain, of chain of particles, with exponential potential of interaction between neighbors. These concepts are named afterMorikazu Toda...

or self-pulsation
Self-pulsation
Self-pulsation takes place at the beginning of laser action.As the pump is switched on, the gainin the active medium rises and exceeds the steady-state value...

(pulsation of output power of laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

at frequencies 104 Hz – 106 Hz in the transient regime)
• Quantum oscillator may refer to an optical local oscillator
Local oscillator
A local oscillator is an electronic device used to generate a signal normally for the purpose of converting a signal of interest to a different frequency using a mixer. This process of frequency conversion, also referred to as heterodyning, produces the sum and difference frequencies of the...

, as well as to a usual model in quantum optics
Quantum optics
Quantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter.- History of quantum optics :...

.

Biological

A circadian rhythm, popularly referred to as body clock, is an endogenously driven , roughly 24-hour cycle in biochemical, physiological, or behavioural processes. Circadian rhythms have been widely observed in plants, animals, fungi and cyanobacteria...

Circadian oscillators are components of the biological clocks that regulate the activities of organisms in relation to environmental cycles and provide an internal temporal framework...

• Lotka–Volterra equation
• Neural oscillation
• Oscillating gene
Oscillating gene
In molecular biology, an oscillating gene or clock gene is a gene that is expressed in an oscillating pattern, often circadian....

• Segmentation oscillator

Human

• Neural oscillation
• Insulin release oscillations
• Pilot-induced oscillation
Pilot-induced oscillation
Pilot-induced oscillations, as defined by MIL-HDBK-1797A, are sustained or uncontrollable oscillations resulting from efforts of the pilot to control the aircraft and occurs when the pilot of an aircraft inadvertently commands an often increasing series of corrections in opposite directions, each...

• Voice production

Economic and social

The term business cycle refers to economy-wide fluctuations in production or economic activity over several months or years...

• Generation gap
Generation gap
The generational gap is and was a term popularized in Western countries during the 1960s referring to differences between people of a younger generation and their elders, especially between children and parents....

• Malthusian economics
• News cycle

Climate and geophysics

The Atlantic multidecadal oscillation is a mode of variability occurring in the North Atlantic Ocean and which has its principal expression in the sea surface temperature field...

• Chandler wobble
Chandler wobble
The Chandler wobble is a small motion in the Earth's axis of rotation relative to the Earth's surface, which was discovered by American astronomer Seth Carlo Chandler in 1891. It amounts to on the Earth's surface and has a period of 433 days...

• Climate oscillation
Climate oscillation
A climate oscillation is any oscillation within global or regional climate. These fluctuations in atmospheric temperature, sea surface temperature, precipitation or other parameters can be quasi-periodic, often occurring on inter-annual, multi-annual, decadal, multidecadal, century-wide, millennial...

• El Niño-Southern Oscillation
El Niño-Southern Oscillation
El Niño/La Niña-Southern Oscillation, or ENSO, is a quasiperiodic climate pattern that occurs across the tropical Pacific Ocean roughly every five years...

The Pacific Decadal Oscillation is a pattern of Pacific climate variability that shifts phases on at least inter-decadal time scale, usually about 20 to 30 years. The PDO is detected as warm or cool surface waters in the Pacific Ocean, north of 20° N...

• Quasi-biennial oscillation
Quasi-biennial oscillation
The quasi-biennial oscillation is a quasi-periodic oscillation of the equatorial zonal wind between easterlies and westerlies in the tropical stratosphere with a mean period of 28 to 29 months. The alternating wind regimes develop at the top of the lower stratosphere and propagate downwards at...

Chemical

• Belousov–Zhabotinsky reaction
• Mercury beating heart
Mercury beating heart
The mercury beating heart is an electrochemical redox reaction between the elements mercury, iron and chromium. The reaction causes a blob of mercury in water to oscillate....

• Briggs–Rauscher reaction
• Bray–Liebhafsky reaction

• Beat (acoustics)
Beat (acoustics)
In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies....

• BIBO stability
BIBO stability
In electrical engineering, specifically signal processing and control theory, BIBO stability is a form of stability for linear signals and systems that take inputs. BIBO stands for Bounded-Input Bounded-Output...

• Critical speed
Critical speed
In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity which excites the natural frequency of a rotating object, such as a shaft, propeller, leadscrew, or gear. As the speed of rotation approaches the object's natural frequency, the object begins...

• Cycle (music)
Cycle (music)
A music cycle is when a section of a song/music is repeated.In music a cycle is a section which is repeated or repeatable indefinitely, with the end of a preceding repetition leading to the beginning of a succeeding repetition. Cycles may be melodic, harmonic, rhythmic, or based on some other...

• Dynamical system
Dynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...

• Earthquake engineering
Earthquake engineering
Earthquake engineering is the scientific field concerned with protecting society, the natural and the man-made environment from earthquakes by limiting the seismic risk to socio-economically acceptable levels...

• Feedback
Feedback
Feedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...

• Frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

• Oscillation (mathematics)
Oscillation (mathematics)
In mathematics, oscillation is the behaviour of a sequence of real numbers or a real-valued function, which does not converge, but also does not diverge to +∞ or −∞; that is, oscillation is the failure to have a limit, and is also a quantitative measure for that.Oscillation is defined as the...

• Oscillator phase noise
Oscillator Phase Noise
Oscillators inherently produce high levels of phase noise. That noise increases at frequencies close to the oscillation frequency or its harmonics. With the noise being close to the oscillation frequency, it cannot be removed by filtering without also removing the oscillation signal...

• Periodic function
Periodic function
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...

• Phase noise
Phase noise
Phase noise is the frequency domain representation of rapid, short-term, random fluctuations in the phase of a waveform, caused by time domain instabilities...

• Reciprocating motion
Reciprocating motion
Reciprocating motion, also called reciprocation, is a repetitive up-and-down or back-and-forth motion. It is found in a wide range of mechanisms, including reciprocating engines and pumps. The two opposite motions that comprise a single reciprocation cycle are called strokes...

• Resonator
Resonator
A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical...

• Rhythm
Rhythm
Rhythm may be generally defined as a "movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions." This general meaning of regular recurrence or pattern in time may be applied to a wide variety of cyclical natural phenomena having a periodicity or...

• Seasonality
Seasonality
In statistics, many time series exhibit cyclic variation known as seasonality, periodic variation, or periodic fluctuations. This variation can be either regular or semi regular....

• Self-exciting oscillation

• Self oscillation
• Signal generator
Signal generator
Signal generators, also known variously as function generators, RF and microwave signal generators, pitch generators, arbitrary waveform generators, digital pattern generators or frequency generators are electronic devices that generate repeating or non-repeating electronic signals...

• Strange attractor
• Structural stability
Structural stability
In mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by C1-small perturbations....

• Tuned mass damper
Tuned mass damper
A tuned mass damper, also known as an active mass damper or harmonic absorber, is a device mounted in structures to reduce the amplitude of mechanical vibrations. Their application can prevent discomfort, damage, or outright structural failure...

• Vibration
Vibration
Vibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...

• Vibrator (mechanical)
Vibrator (mechanical)
A vibrator is a mechanical device to generate vibrations. The vibration is often generated by an electric motor with an unbalanced mass on its driveshaft.There are many different types of vibrator...