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. For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Familiar examples include a swinging pendulum and AC power. A pendulum is a mass that is attached to a pivot from which it can swing freely An alternating current ( AC) is an Electric current whose direction reverses cyclically as opposed to Direct current, whose direction remains constant The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes is used to be synonymous with "oscillation. Vibration refers to mechanical Oscillations about an equilibrium point. " Oscillations occur not only in physical systems but also in biological systems and in human society. Ecology (from Greek grc οἶκος oikos, "house(hold" and grc -λογία -logia) is the scientific study of A society is a Population of Humans characterized by patterns of relationships between individuals that share a distinctive Culture and Institutions

Contents 1 Simplicity 2 Damped, driven and self-induced oscillations 3 Coupled oscillations 4 Continuous systems - waves 5 Examples 5.1 Mechanical 5.2 Electrical 5.3 Electro-mechanical 5.4 Optical 5.5 Biological 5.6 Human 5.7 Economic and social 5.8 Climate and geophysics 5.9 Chemical 6 See also 7 External links

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. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object The word linear comes from the Latin word linearis, which means created by lines. A spring is a flexible elastic object used to store mechanical Energy. In Physics, a force is whatever can cause an object with Mass to Accelerate. Gravitation is a natural Phenomenon by which objects with Mass attract one another 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. In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product 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 physics the term dynamics customarily refers to the time evolution of physical processes This article is about the harmonic oscillator in classical mechanics Frequency is a measure of the number of occurrences of a repeating event per unit Time. Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. 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. Statics is the branch of Mechanics concerned with the analysis of loads ( Force, torque/moment) on Physical systems in Static equilibrium The kinetic energy of an object is the extra Energy which it possesses due to its motion Potential energy can be thought of as Energy stored within a physical system 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. This article is about the harmonic oscillator in classical mechanics In mathematics Fourier analysis is a subject area which grew out of the study of Fourier series

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. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which Thermal energy is the sum of the sensible energy and latent energy. 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. An electronic circuit is a closed path formed by the interconnection of Electronic components through which an Electric current can flow 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. FLUID ( F ast L ight '''U'''ser '''I'''nterface D esigner is a graphical editor that is used to produce FLTK Source code 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. WING "ESPN 1410" is a commercial AM radio station in Dayton Ohio operating with 5000 watts at 1410 kHz with studios offices and transmitter located on David Angle of attack ( AOA, \alpha Greek letter alpha) is a term used in Aerodynamics to describe the Angle between the Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five The lift coefficient ( CL or CZ) is a non-dimensional coefficient that relates the lift generated by an Airfoil, the At sufficiently large displacements, the stiffness of the wing dominates to provide the restoring force that enables an oscillation. Stiffness is the resistance of an elastic body to Deformation by an applied Force.

Coupled oscillations

The harmonic oscillator and the systems it models have a single degree of freedom. For information on degrees of freedom in other sciences see Degrees 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. 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

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 is a common Chemical substance that is essential for the survival of all known forms of Life. 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. The classical limit is the ability of a physical theory to approximate or "recover" Classical mechanics when considered over special values of its parameters Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness A wave is a disturbance that propagates through Space and Time, usually with transference of Energy.

Examples

See also

External links

• Interactive Java Tutorial on Electronic Oscillators National High Magnetic Field Laboratory
• Vibrations - a chapter from an online textbook
• Dealing Vibration at work

The Lotka–Volterra equations, also known as the predator-prey equations, are a pair of first order Non-linear, Differential equations frequently used The concept of neural Oscillations is close to the concept of Brain waves. Pilot-induced oscillation occurs when the pilot of an Aircraft inadvertently commands an often increasing series of corrections in opposite directions each an The voice organ is the part of the Human body responsible for the generation of Sound, usually in the form of speech or Singing. The insulin concentration in blood increases after meals and gradually returns to basal levels during 1-2 hours The term business cycle or economic cycle refers to the fluctuations of economic activity during its long term growth trend A generation gap is a popular term used to describe big differences between people of a younger generation and their elders Thomas Robert Malthus FRS (13 February 1766 – 23 December 1834 was an English political economist and demographer who expressed views The 24-hour news cycle is a term for the faster pace of News and information which arrived in society with the advent of Cable news channels as opposed to the day Climate encompasses the temperatures humidity rainfall atmospheric particle count and numerous other meteorogical factors in a given region over long periods of 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 El Niño-Southern Oscillation ( ENSO; commonly referred to as simply El Niño) is a global coupled ocean-atmosphere phenomenon The QBO ( quasi-biennial oscillation) is a quasi- periodic oscillation of the Equatorial Zonal Wind between easterlies and westerlies Characteristics A tide is a repeated cycle of sea level changes in the following stages Over several hours the water rises or advances up a beach in the flood EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 An ocean (from Greek, ''Okeanos'' (Oceanus) is a major body of saline water, and a principal component of the Hydrosphere. A Belousov-Zhabotinsky reaction, or BZ reaction, is one of a class of reactions that serve as a classical example of Non-equilibrium thermodynamics, resulting in the The mercury beating heart is an electrochemical reaction of the element mercury to iron and an electrolyte Bibo redirects here For the Egyptian football player nicknamed Bibo see Mahmoud El-Khateeb. In Solid mechanics, in the field of Rotordynamics, the critical speed is the theoretical Angular velocity which excites the Natural frequency The dynamical system concept is a mathematical Formalization for any fixed "rule" which describes the Time dependence of a point's position Feedback is a circular causal Process whereby some proportion of a system's output is returned (fed back to the Input. In Mathematics, oscillation is the behaviour of a Sequence of Real numbers or a real-valued function, which does not converge, In Mathematics, a periodic function is a function that repeats its values after some definite period has been added to its Independent variable Rhythm (from Greek ῥυθμός - rhythmos, "any measured flow or movement symmetry" is the variation of the length and accentuation of Self oscillation is a term usually used when describing a voltage controlled filter of an Analog synthesizer. A signal generator, also known variously as a test signal generator, function generator, tone generator, arbitrary waveform generator, digital An attractor is a set to which a Dynamical system evolves after a long enough time In Mathematics, structural stability is an aspect of Stability theory concerning whether a given function is sensitive to a small perturbation. The categorization of Time into discrete named blocks is called Periodization. A tuned mass damper, also known as an active mass damper ( AMD) or harmonic absorber, is a device mounted in structures to prevent discomfort damage or Vibration refers to mechanical Oscillations about an equilibrium point. A vibrator is a mechanical device that is designed to generate vibrations The vibration is often generated by an Electric motor with an unbalanced

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