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Oscillation is the repetitive or periodic variation, typically in
time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...
, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging
pendulum A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the ...
and
alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
. Oscillations can be used in physics to approximate complex interactions, such as those between atoms. Oscillations occur not only in mechanical systems but also in
dynamic system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...
s in virtually every area of science: for example the beating of the
human heart The heart is a muscular organ in most animals. This organ pumps blood through the blood vessels of the circulatory system. The pumped blood carries oxygen and nutrients to the body, while carrying metabolic waste such as carbon dioxide to ...
(for circulation),
business cycle Business cycles are intervals of Economic expansion, expansion followed by recession in economic activity. These changes have implications for the welfare of the broad population as well as for private institutions. Typically business cycles are ...
s in
economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and intera ...
, predator–prey population cycles in
ecology Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps wi ...
, geothermal
geyser A geyser (, ) is a spring characterized by an intermittent discharge of water ejected turbulently and accompanied by steam. As a fairly rare phenomenon, the formation of geysers is due to particular hydrogeological conditions that exist only in ...
s in
geology Geology () is a branch of natural science concerned with Earth and other astronomical objects, the features or rocks of which it is composed, and the processes by which they change over time. Modern geology significantly overlaps all other Ear ...
, vibration of strings in
guitar The guitar is a fretted musical instrument that typically has six strings. It is usually held flat against the player's body and played by strumming or plucking the strings with the dominant hand, while simultaneously pressing selected stri ...
and other
string instrument String instruments, stringed instruments, or chordophones are musical instruments that produce sound from vibrating strings when a performer plays or sounds the strings in some manner. Musicians play some string instruments by plucking the ...
s, periodic firing of
nerve cell A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. No ...
s in the brain, and the periodic swelling of
Cepheid variable A Cepheid variable () is a type of star that pulsates radially, varying in both diameter and temperature and producing changes in brightness with a well-defined stable period and amplitude. A strong direct relationship between a Cepheid varia ...
stars in
astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
. The term ''
vibration Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic function, periodic, such as the motion of a pendulum ...
'' is precisely used to describe a mechanical oscillation. Oscillation, especially rapid oscillation, may be an undesirable phenomenon in
process control An industrial process control in continuous production processes is a discipline that uses industrial control systems to achieve a production level of consistency, economy and safety which could not be achieved purely by human manual control. I ...
and
control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
(e.g. in
sliding mode control In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces the system to "sl ...
), where the aim is
convergence Convergence may refer to: Arts and media Literature *''Convergence'' (book series), edited by Ruth Nanda Anshen * "Convergence" (comics), two separate story lines published by DC Comics: **A four-part crossover storyline that united the four Wei ...
to stable state. In these cases it is called chattering or flapping, as in
valve A valve is a device or natural object that regulates, directs or controls the flow of a fluid (gases, liquids, fluidized solids, or slurries) by opening, closing, or partially obstructing various passageways. Valves are technically fittings ...
chatter, and
route flapping In computer networking and telecommunications, route flapping occurs when a router alternately advertises a destination network via one route then another, or as unavailable and then available again, in quick sequence. Route flapping is caused b ...
.


Simple harmonic

The simplest mechanical oscillating system is a
weight In science and engineering, the weight of an object is the force acting on the object due to gravity. Some standard textbooks define weight as a Euclidean vector, vector quantity, the gravitational force acting on the object. Others define weigh ...
attached to a
linear Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear r ...
spring Spring(s) may refer to: Common uses * Spring (season), a season of the year * Spring (device), a mechanical device that stores energy * Spring (hydrology), a natural source of water * Spring (mathematics), a geometric surface in the shape of a ...
subject to only
weight In science and engineering, the weight of an object is the force acting on the object due to gravity. Some standard textbooks define weight as a Euclidean vector, vector quantity, the gravitational force acting on the object. Others define weigh ...
and
tension Tension may refer to: Science * Psychological stress * Tension (physics), a force related to the stretching of an object (the opposite of compression) * Tension (geology), a stress which stretches rocks in two opposite directions * Voltage or el ...
. 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 mass back to the equilibrium position, it has acquired
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
which keeps it moving beyond that position, establishing a new restoring force in the opposite sense. If a constant
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
such as
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
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 systems where the restoring force on a body is directly proportional to its displacement, such as the dynamics of the spring-mass system, are described mathematically by the
simple harmonic oscillator In mechanics and physics, simple harmonic motion (sometimes abbreviated ) is a special type of periodic motion of a body resulting from a dynamic equilibrium between an inertial force, proportional to the acceleration of the body away from the ...
and the regular periodic motion is known as
simple harmonic motion In mechanics and physics, simple harmonic motion (sometimes abbreviated ) is a special type of periodic motion of a body resulting from a dynamic equilibrium between an inertial force, proportional to the acceleration of the body away from the ...
. In the spring-mass system, oscillations occur because, at the
static Static may refer to: Places *Static Nunatak, a nunatak in Antarctica United States * Static, Kentucky and Tennessee *Static Peak, a mountain in Wyoming **Static Peak Divide, a mountain pass near the peak Science and technology Physics *Static el ...
equilibrium displacement, the mass has
kinetic energy In physics, the kinetic energy of an object is the energy that 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 accele ...
which is converted into
potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potentia ...
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. In the case of the spring-mass system,
Hooke's law In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring (device), spring by some distance () Proportionality (mathematics)#Direct_proportionality, scales linearly with respect to that ...
states that the restoring force of a spring is: F = -kx By using
Newton's second law Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motion ...
, the differential equation can be derived: \ddot = -\frac km x = -\omega^2 x, where \omega = \sqrt The solution to this differential equation produces a sinusoidal position function: x(t) = A \cos (\omega t - \delta) where is the frequency of the oscillation, is the amplitude, and is the
phase shift In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it v ...
of the function. These are determined by the initial conditions of the system. Because cosine oscillates between 1 and −1 infinitely, our spring-mass system would oscillate between the positive and negative amplitude forever without friction.


Two-dimensional oscillators

In two or three dimensions, harmonic oscillators behave similarly to one dimension. The simplest example of this is an
isotropic Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
oscillator, where the restoring force is proportional to the displacement from equilibrium with the same restorative constant in all directions. F = -k\vec This produces a similar solution, but now there is a different equation for every direction. \begin x(t) &= A_x \cos(\omega t - \delta _x), \\ y(t) &= A_y \cos(\omega t - \delta_y), \\ & \;\, \vdots \end


Anisotropic oscillators

With
anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
oscillators, different directions have different constants of restoring forces. The solution is similar to isotropic oscillators, but there is a different frequency in each direction. Varying the frequencies relative to each other can produce interesting results. For example, if the frequency in one direction is twice that of another, a figure eight pattern is produced. If the ratio of frequencies is irrational, the motion is
quasiperiodic Quasiperiodicity is the property of a system that displays irregular periodicity. Periodic behavior is defined as recurring at regular intervals, such as "every 24 hours". Quasiperiodic behavior is a pattern of recurrence with a component of unpred ...
. This motion is periodic on each axis, but is not periodic with respect to r, and will never repeat.


Damped oscillations

All real-world oscillator systems are thermodynamically irreversible. This means there are dissipative processes such as
friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of t ...
or
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels ...
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. Damped oscillators are created when a resistive force is introduced, which is dependent on the first derivative of the position, or in this case velocity. The differential equation created by Newton's second law adds in this resistive force with an arbitrary constant . This example assumes a linear dependence on velocity. m\ddot + b\dot + kx = 0 This equation can be rewritten as before: \ddot + 2 \beta \dot + \omega_0^2x = 0, where 2 \beta = \frac b m. This produces the general solution: x(t) = e^ \left(C_1e^ + C_2 e^\right), where \omega_1 = \sqrt. The exponential term outside of the parenthesis is the decay function and is the damping coefficient. There are 3 categories of damped oscillators: under-damped, where ; over-damped, where ; and critically damped, where .


Driven oscillations

In addition, an oscillating system may be subject to some external force, as when an AC circuit is connected to an outside power source. In this case the oscillation is said to be '' driven''. The simplest example of this is a spring-mass system with a
sinusoidal A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in m ...
driving force. \ddot + 2 \beta\dot + \omega_0^2 x = f(t),where f(t) = f_0 \cos(\omega t + \delta). This gives the solution: x(t) = A \cos(\omega t - \delta) + A_ \cos(\omega_1 t - \delta_), where A = \sqrt and \delta = \tan^\left(\frac \right) The second term of is the transient solution to the differential equation. The transient solution can be found by using the initial conditions of the system. Some systems can be excited by energy transfer from the environment. This transfer typically occurs where systems are embedded in some
fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
flow. For example, the phenomenon of flutter in
aerodynamics Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...
occurs when an arbitrarily small displacement of an
aircraft An aircraft is a vehicle that is able to fly by gaining support from the air. It 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 ...
wing A wing is a type of fin that produces lift while moving through air or some other fluid. Accordingly, wings have streamlined cross-sections that are subject to aerodynamic forces and act as airfoils. A wing's aerodynamic efficiency is expres ...
(from its equilibrium) results in an increase in the
angle of attack In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is m ...
of the wing on the air flow and a consequential increase in
lift coefficient In fluid dynamics, the lift coefficient () is a dimensionless quantity that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area. A lifting body is a foil or a com ...
, leading to a still greater displacement. At sufficiently large displacements, the
stiffness Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Calculations The stiffness, k, of a b ...
of the wing dominates to provide the restoring force that enables an oscillation.


Resonance

Resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
occurs in a damped driven oscillator when ω = ω0, that is, when the driving frequency is equal to the natural frequency of the system. When this occurs, the denominator of the amplitude is minimized, which maximizes the amplitude of the oscillations.


Coupled oscillations

The harmonic oscillator and the systems it models have a single
degree of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...
. 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 A phenomenon ( : phenomena) is an observable event. The term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be directly observed. Kant was heavily influenced by Gottfried W ...
was first observed by
Christiaan Huygens Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists of ...
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 A normal mode of a dynamical 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 free motion described by the normal modes takes place at fixed frequencies. ...
s. The simplest form of coupled oscillators is a 3 spring, 2 mass system, where masses and spring constants are the same. This problem begins with deriving Newton's second law for both masses. \begin m_1 \ddot_1 = -(k_1 + k_2)x_1 + k_2 x_2 \\ m_2\ddot_2 = k_2 x_1 - (k_2+k_3)x_2 \end The equations are then generalized into matrix form. F = M\ddot = kx, where M=\begin m_1 & 0 \\ 0 & m_2 \end, x = \begin x_1 \\ x_2 \end, and k = \begin k_1+k_2 & -k_2 \\ -k_2 & k_2+k_3 \end The values of and can be substituted into the matrices. \begin m_1=m_2=m ,\;\; k_1=k_2=k_3=k, \\ M = \begin m & 0 \\ 0 & m \end, \;\; k=\begin 2k & -k \\ -k & 2k \end \end These matrices can now be plugged into the general solution. \begin \left(k-M \omega^2\right) a &= 0 \\ \begin 2k-m \omega^2 & -k \\ -k & 2k - m \omega^2 \end &= 0 \end The determinant of this matrix yields a quadratic equation. \begin &\left(3k-m \omega^2\right)\left(k-m \omega^2\right)= 0 \\ &\omega_1 = \sqrt , \;\; \omega_2 = \sqrt \end Depending on the starting point of the masses, this system has 2 possible frequencies (or a combination of the two). If the masses are started with their displacements in the same direction, the frequency is that of a single mass system, because the middle spring is never extended. If the two masses are started in opposite directions, the second, faster frequency is the frequency of the system. More special cases are the coupled oscillators where energy alternates between two forms of oscillation. Well-known is the
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 mechanica ...
, where the oscillation alternates between the elongation of a vertical spring and the rotation of an object at the end of that spring. Coupled oscillators are a common description of two related, but different phenomena. One case is where both oscillations affect each other mutually, which usually leads to the occurrence of a single, entrained oscillation state, where both oscillate with a ''compromise frequency''. Another case is where one external oscillation affects an internal oscillation, but is not affected by this. In this case the regions of synchronization, known as
Arnold Tongues In mathematics, particularly in dynamical systems, Arnold tongues (named after Vladimir Arnold) Section 12 in page 78 has a figure showing Arnold tongues. are a pictorial phenomenon that occur when visualizing how the rotation number of a dynami ...
, can lead to highly complex phenomena as for instance chaotic dynamics.


Small oscillation approximation

In physics, a system with a set of conservative forces and an equilibrium point can be approximated as a harmonic oscillator near equilibrium. An example of this is the
Lennard-Jones potential The Lennard-Jones potential (also termed the LJ potential or 12-6 potential) is an intermolecular pair potential. Out of all the intermolecular potentials, the Lennard-Jones potential is probably the one that has been the most extensively studied ...
, where the potential is given by: U(r) = U_0 \left \left(\frac r \right)^ - \left(\frac r \right)^6 \right/math> The equilibrium points of the function are then found: \begin \frac &= 0 = U_0 \left 12 r_0^ r^ + 6r_0^6r^\right\\ \Rightarrow r &\approx r_0 \end The second derivative is then found, and used to be the effective potential constant: \begin \gamma_\text &= \left.\frac \_ = U_0 \left 12(13) r_0^ r^ - 6 (7) r_0^6 r^ \right\\ ex&= \frac \end The system will undergo oscillations near the equilibrium point. The force that creates these oscillations is derived from the effective potential constant above: F= - \gamma_\text(r-r_0) = m_\text \ddot r This differential equation can be re-written in the form of a simple harmonic oscillator: \ddot r + \frac (r-r_0) = 0 Thus, the frequency of small oscillations is: \omega_0 = \sqrt = \sqrt Or, in general form \omega_0 = \sqrt This approximation can be better understood by looking at the potential curve of the system. By thinking of the potential curve as a hill, in which, if one placed a ball anywhere on the curve, the ball would roll down with the slope of the potential curve. This is true due to the relationship between potential energy and force. \frac = - F(r) By thinking of the potential in this way, one will see that at any local minimum there is a "well" in which the ball would roll back and forth (oscillate) between r_\text and r_\text. This approximation is also useful for thinking of
Kepler orbits Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws o ...
.


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 Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...
. Such systems have (in the
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 n ...
) an
infinite Infinite may refer to: Mathematics *Infinite set, a set that is not a finite set *Infinity, an abstract concept describing something without any limit Music * Infinite (group), a South Korean boy band *''Infinite'' (EP), debut EP of American m ...
number of normal modes and their oscillations occur in the form of waves that can characteristically propagate.


Mathematics

The mathematics of oscillation deals with the quantification of the amount that a sequence or function tends to move between extremes. There are several related notions: oscillation of a
sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is calle ...
of
real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...
s, oscillation of a real-valued
function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...
at a point, and oscillation of a function on an interval (or
open set In mathematics, open sets are a generalization of open intervals in the real line. In a metric space (a set along with a distance defined between any two points), open sets are the sets that, with every point , contain all points that are suf ...
).


Examples


Mechanical

*
Double pendulum In physics and mathematics, in the area of dynamical systems, a double pendulum also known as a chaos pendulum is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a ...
*
Foucault pendulum The Foucault pendulum or Foucault's pendulum is a simple device named after French physicist Léon Foucault, conceived as an experiment to demonstrate the Earth's rotation. A long and heavy pendulum suspended from the high roof above a circular a ...
*
Helmholtz resonator Helmholtz resonance or wind throb 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'', wh ...
*Oscillations in the Sun (
helioseismology Helioseismology, a term coined by Douglas Gough, is the study of the structure and dynamics of the Sun through its oscillations. These are principally caused by sound waves that are continuously driven and damped by convection near the Sun's surfa ...
), stars (
asteroseismology Asteroseismology or astroseismology is the study of oscillations in stars. Stars have many resonant modes and frequencies, and the path of sound waves passing through a star depends on the speed of sound, which in turn depends on local temperature ...
) and
Neutron-star oscillations Asteroseismology studies the internal structure of the Sun and other stars using oscillations. These can be studied by interpreting the temporal frequency spectrum acquired through observations. In the same way, the more extreme neutron stars migh ...
. *
Quantum harmonic oscillator 量子調和振動子 は、 古典調和振動子 の 量子力学 類似物です。任意の滑らかな ポテンシャル は通常、安定した 平衡点 の近くで 調和ポテンシャル として近似できるため、最 ...
* Playground swing *
String instrument String instruments, stringed instruments, or chordophones are musical instruments that produce sound from vibrating strings when a performer plays or sounds the strings in some manner. Musicians play some string instruments by plucking the ...
s *
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 contr ...
*
Tuning fork A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it against ...
*
Vibrating string A vibration in a strings (music), string is a wave. Acoustic resonance#Resonance of a string, Resonance causes a vibrating string to produce a sound with constant frequency, i.e. constant pitch (music), pitch. If the length or tension of the strin ...
*
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 mechanica ...
*
Lever escapement The lever escapement, invented by the English clockmaker Thomas Mudge in 1754 (albeit first used in 1769), is a type of escapement that is used in almost all mechanical watches, as well as small mechanical non-pendulum clocks, alarm clocks, an ...


Electrical

*
Alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
* Armstrong (or Tickler or Meissner) oscillator * Astable multivibrator * Blocking oscillator * Butler oscillator *
Clapp oscillator The Clapp oscillator or Gouriet oscillator is an LC electronic oscillator that uses a particular combination of an inductor and three capacitors to set the oscillator's frequency. LC oscillators use a transistor (or vacuum tube or other gain eleme ...
*
Colpitts oscillator A Colpitts oscillator, invented in 1918 by American engineer Edwin H. Colpitts, is one of a number of designs for LC oscillators, electronic oscillators that use a combination of inductors (L) and capacitors (C) to produce an oscillation at a certa ...
*
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 l ...
*
Electronic oscillator An electronic oscillator is an electronic circuit that produces a periodic, oscillation, oscillating electronic signal, often a sine wave or a square wave or a triangle wave. Oscillation, Oscillators convert direct current (DC) from a power supp ...
*
Extended interaction oscillator The extended interaction oscillator (EIO) is a linear-beam vacuum tube designed to convert direct current to RF power. The conversion mechanism is the space charge wave process whereby velocity modulation in an electron beam transforms to cur ...
*
Hartley oscillator The Hartley oscillator is an electronic oscillator circuit in which the oscillation frequency is determined by a tuned circuit consisting of capacitors and inductors, that is, an LC oscillator. The circuit was invented in 1915 by American enginee ...
*
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. The basic princ ...
*
Phase-shift oscillator A phase-shift oscillator is a linear electronic oscillator circuit that produces a sine wave output. It consists of an inverting amplifier element such as a transistor or op amp with its output fed back to its input through a phase-shift network c ...
*
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 (1872–1956), the Pierce oscillator is a derivative of the Colpitts ...
*
Relaxation oscillator In electronics a relaxation oscillator is a nonlinear electronic oscillator circuit that produces a nonsinusoidal repetitive output signal, such as a triangle wave or square wave. on Peter Millet'Tubebookswebsite The circuit consists of a feedba ...
*
RLC circuit An RLC circuit is an electrical circuit consisting of a electrical resistance, resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the ...
*
Royer oscillator A Royer oscillator is an electronic relaxation oscillator that employs a saturable-core transformer in the main power path. It was invented and patented in April 1954 by Richard L. Bright & George H. Royer, who are listed as co-inventors on the ...
* Vačkář 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 for the measurement of impe ...


Electro-mechanical

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Crystal oscillator A crystal oscillator is an electronic oscillator circuit that uses a piezoelectric crystal as a frequency-selective element. The oscillator frequency is often used to keep track of time, as in quartz wristwatches, to provide a stable cloc ...


Optical

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Laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
(oscillation of
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical c ...
with frequency of order 1015 Hz) *
Oscillator Toda In physics, the Toda oscillator is a special kind of nonlinear oscillator. It represents a chain of particles with exponential potential interaction between neighbors. These concepts are named after Morikazu Toda. The Toda oscillator is used a ...
or
self-pulsation Self-pulsation is a transient phenomenon in continuous-wave lasers. Self-pulsation takes place at the beginning of laser action. As the pump is switched on, the gain in the active medium rises and exceeds the steady-state value. The number of p ...
(pulsation of output power of
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
at frequencies 104 Hz – 106 Hz in the transient regime) *
Quantum oscillator 量子調和振動子 は、 古典調和振動子 の 量子力学 類似物です。任意の滑らかな ポテンシャル は通常、安定した 平衡点 の近くで 調和ポテンシャル として近似できるため、最 ...
may refer to an optical
local oscillator In electronics, a local oscillator (LO) is an electronic oscillator used with a mixer to change the frequency of a signal. This frequency conversion process, also called heterodyning, produces the sum and difference frequencies from the frequenc ...
, as well as to a usual model in
quantum optics Quantum optics is a branch of atomic, molecular, and optical physics dealing with how individual quanta of light, known as photons, interact with atoms and molecules. It includes the study of the particle-like properties of photons. Photons have b ...
.


Biological

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Circadian rhythm A circadian rhythm (), or circadian cycle, is a natural, internal process that regulates the sleep–wake cycle and repeats roughly every 24 hours. It can refer to any process that originates within an organism (i.e., Endogeny (biology), endogeno ...
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Bacterial Circadian Rhythms Bacterial circadian rhythms, like other circadian rhythms, are endogenous "biological clocks" that have the following three characteristics: (a) in constant conditions (i.e. constant temperature and either constant light or constant darkness ) the ...
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Circadian oscillator A circadian clock, or circadian oscillator, is a biochemical oscillator that cycles with a stable phase and is synchronized with solar time. Such a clock's ''in vivo'' period is necessarily almost exactly 24 hours (the earth's current solar day ...
* Lotka–Volterra equation *
Neural oscillation Neural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by ...
*
Oscillating gene In molecular biology, an oscillating gene is a gene that is expressed in a rhythmic pattern or in periodic cycles. Oscillating genes are usually circadian and can be identified by periodic changes in the state of an organism. Circadian rhythms, c ...
*
Segmentation clock Segment or segmentation may refer to: Biology *Segmentation (biology), the division of body plans into a series of repetitive segments ** Segmentation in the human nervous system * Internodal segment, the portion of a nerve fiber between two Nodes ...


Human oscillation

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Neural oscillation Neural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by ...
* Insulin release oscillations * gonadotropin releasing hormone pulsations *
Pilot-induced oscillation Pilot-induced oscillations (PIOs), as defined by MIL-HDBK-1797A, are ''sustained or uncontrollable oscillations resulting from efforts of the pilot to control the aircraft''. They occur when the pilot of an aircraft inadvertently commands an oft ...
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Voice production In articulatory phonetics, the place of articulation (also point of articulation) of a consonant is a location along the vocal tract where its production occurs. It is a point where a constriction is made between an active and a passive articula ...


Economic and social

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Business cycle Business cycles are intervals of Economic expansion, expansion followed by recession in economic activity. These changes have implications for the welfare of the broad population as well as for private institutions. Typically business cycles are ...
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Generation gap A generation gap or generational gap is a difference of opinions between one generation and another regarding beliefs, politics, or values. In today's usage, ''generation gap'' often refers to a perceived gap between younger people and their paren ...
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Malthusian Malthusianism is the idea that population growth is potentially exponential while the growth of the food supply or other resources is linear, which eventually reduces living standards to the point of triggering a population die off. This event, c ...
economics *News cycle


Climate and geophysics

*Atlantic multidecadal oscillation *Chandler wobble *Climate oscillation *El Niño-Southern Oscillation *Pacific decadal oscillation *Quasi-biennial oscillation


Astrophysics

*Neutron-star oscillations, Neutron stars *Cyclic Model


Quantum mechanical

*Neutral particle oscillation, e.g. neutrino oscillations *
Quantum harmonic oscillator 量子調和振動子 は、 古典調和振動子 の 量子力学 類似物です。任意の滑らかな ポテンシャル は通常、安定した 平衡点 の近くで 調和ポテンシャル として近似できるため、最 ...


Chemical

*Belousov–Zhabotinsky reaction *Mercury beating heart *Briggs–Rauscher reaction *Bray–Liebhafsky reaction


Computing

*Oscillator (cellular_automaton), Cellular Automata oscillator


See also

*Antiresonance *Beat (acoustics) *BIBO stability *Critical speed *Cycle (music) *Dynamical system *Earthquake engineering *Feedback *Fourier transform for computing periodicity in evenly spaced data *Frequency *Hidden oscillation *Least-squares spectral analysis for computing periodicity in unevenly spaced data *Oscillator phase noise *Periodic function *Phase noise *Quasiperiodicity *Reciprocating motion *Resonator *Rhythm *Seasonality *Self-oscillation *Signal generator *Squegging *Strange attractor *Structural stability *Tuned mass damper *Vibration *Vibrator (mechanical)


References


External links

*
Vibrations
nbsp;– a chapter from an online textbook {{Authority control Oscillation,