NationMaster - Encyclopedia: Oscillator

Oscillation is the In mathematics, a periodic function is a function that repeats its values, after adding some definite period to the variable. ...periodic variation, typically in (Clockwise from upper left) Notable Time magazine covers from May 7, 1945; July 25, 1969; December 31, 1999; September 14, 2001; and April 21, 2003. ...time, of some measure as seen, for example, in a swinging A gravity pendulum is a weight on the end of a rigid rod, which, when given some initial lift from the vertical position, will swing back and forth under the influence of gravity over its central (lowest) point. ...pendulum. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes is used to be synonymous with oscillation. Oscillations occur not only in physical systems but also in Ecology is the branch of science that studies the distribution and abundance of living organisms, and the interactions between organisms and their environment. ...biological systems and in human A society is a group of people living or working together. ...society. Oscillations are the origin of the sensation of In music, pitch is the perception of the frequency of a note. ...musical tone.

Contents

1 Simple systems

2 Damped, driven and self_excited oscillations

2.1 Driven oscillations
2.2 Self_exciting systems

3 Coupled oscillations

4 Continuous systems _ waves

5 Examples

5.1 Mechanical
5.2 Electrical
5.3 Electro_mechanical
5.4 Biological
5.5 Human
5.6 Economic and social
5.7 Climate and geophysics

6 See also

Simple systems

The simplest oscillating system is a Mass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. ...mass, subject to the In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ...force of This article covers the physics of gravitation. ...gravity, attached to a The word linear comes from the Latin word linearis, which means created by lines. ...linear A helical or coil spring. ...spring. The system is in an For the 2002 science fiction movie see Equilibrium (2002 movie) Equilibrium or balance is any of a number of related phenomena in the natural and social sciences. ...equilibrium state when the Weight is the force exerted upon an object by virtue of its position in a gravitational field. ...weight of the mass is balanced by the In physics, tension is a force on a body directed to produce strain (extension); it can be considered to be negative compression. ...tension of the spring. 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 Inertia is the tendency of any state of affairs to persist in the absence of external influences. ...inertia which keeps it moving beyond that position, establishing a new restoring force, now in the opposite sense. The specific In mathematics and physics, dynamics is the branch of mechanics that is concerned with the effects of forces on the motion of objects. ...dynamics of this spring_mass system are described mathematically by the A harmonic oscillator is a mechanical system in which there exists a returning force F directly proportionate to the displacement x, i. ...simple harmonic oscillator and the regular In mathematics, a periodic function is a function that repeats its values, after adding some definite period to the variable. ...periodic motion is known as Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. ...simple harmonic motion. In the spring_mass system, oscillations occur because, when at the Statics is the branch of physics that is concerned with physical systems that are 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 rest under the action of external forces of equilibrium. ...static equilibrium displacement, the mass has Kinetic energy (also called vis viva, or living force) is energy possessed by a body by virtue of its motion. ...kinetic energy which is converted into Energy is a fundamental quantity that every physical system possesses; it allows us to predict how much work the system could be made to do, or how much heat it can exchange. ...energy stored in the spring at the extremes of its path.

The spring_mass system illustrates some important and universal principles of oscillation:

Existence of an equilibrium;
Presence of some restoring force (or restoring principle in non_mechanical systems);
Some form of "inertia" that maintains motion; and
Exchange in "energy" between that associated with "inertia" and that of the restoring force.

The A harmonic oscillator is a mechanical system in which there exists a returning force F directly proportionate to the displacement x, i. ...harmonic oscillator offers a model of many more complicated types of oscillation and can be extended by the use of Harmonic analysis is the branch of mathematics which studies the representation of functions or signals as the superposition of basic waves. ...Fourier analysis.

Damped, driven and self_excited oscillations

In real_world systems, the In physics, the second law of thermodynamics, in its many forms, is a statement about the quality and direction of energy flow, and it is closely related to the concept of entropy. ...second law of thermodynamics dictates that there is some continual and inevitable conversion of energy into the Thermal energy is kinetic energy due to disordered motions and vibrations of microscopic particles such as molecules and atoms. ...thermal energy of the environment. Thus, damped oscillations tend to decay with time unless there is some net source of energy in the system. The simplest description of this decay process can be illustrated by the A harmonic oscillator is a mechanical system in which there exists a returning force F directly proportionate to the displacement x, i. ...harmonic oscillator.

Driven oscillations

One possible external source of energy is to drive the oscillations, as in exciting the mass_spring system by periodically moving the spring's anchor point. The driving force can be structured, perhaps itself a Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. ...simple harmonic motion, or In ordinary language, the word random is used to express apparent lack of purpose or cause. ...random. In general, the response of the system is not independent of the A period is an arbitrary interval of time. ...period of a simple_harmonic driving force. The amplitude of the system's response tends to be highly_peaked at particular periods, the phenomenon of This article is about resonance in physics. ...resonance.

Self_exciting systems

Some systems are able to extract energy from their environment. This typically occurs where systems are embedded in some FLUID widget list window FLUID (Fast Light User Interface Designer) is a graphical editor that is used to produce FLTK source code. ...fluid flow. For example, the phenomenon of Flutter: In electronics, rapid variation of signal parameters, such as amplitude, phase, and frequency. ...flutter in Aerodynamics is a branch of fluid dynamics concerned with the study of gas flows, first analysed by George Cayley in the 1800s. ...aerodynamics occurs when an, arbitrarily small, displacement of an This article refers to the tool of travel. ...aircraft For some other uses of the word wing please see Wing (disambiguation). ...wing, from its equilibrium, results in an increase in the In this diagram, the black arrow represents the direction of the wind. ...angle of attack of the wing on the This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...air flow and a consequential increase in The coefficient of lift is a number associated with a particular shape of an aerofoil, and is incorporated in the lift equation to predict the lift force generated by a wing using this particular cross section. ...lift coefficient leading to a greater displacement before, at sufficiently large displacements, the Stiffness is the resistance of an elastic body to deflection by an applied force. ...stiffness of the wing dominates to provide the restoring force that enables an oscillation. The phenomenon of Hunting is a self_exciting oscillation of a physical system, commonly that of systems incorporating feedback. ...hunting is a self_exciting oscillation in non_linear electrical circuits.

Coupled oscillations

The A harmonic oscillator is a mechanical system in which there exists a returning force F directly proportionate to the displacement x, i. ...harmonic oscillator, and the more complicated systems for which it stands as a simple model, has a single The phrase degrees of freedom is used in three different branches of science: in physics and physical chemistry, in mechanical and aerospace engineering, and in statistics. ...degree of freedom. More complicated systems have more degrees of freedom, for example two masses and two springs. In such cases, energy is converted between the respective inertias of each degree of freedom and the several restoring forces in the system. 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 in an oscillating system are special solutions where all the parts of the system are oscillating with the same frequency (called normal frequencies or allowed frequencies). ...normal modes.

Continuous systems _ waves

As the number of degrees of freedom becomes indefinitely large, a system approaches In mathematics, a continuous function is one in which arbitrarily small changes in the input produce arbitrarily small changes in the output. ...continuity, for example, a string or the surface of a body of Drinking water This article focuses on water as we experience it every day. ...water. Such systems have an Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ...infinite number of normal modes and their oscillations occur in the form of This article is about waves in the most general sense; a separate article focuses on ocean waves. ...waves that have the characteristic that they can propagate.

Examples

See also: This is a list of wave topics, by Wikipedia page. ...list of wave topics

Mechanical

A gravity pendulum is a weight on the end of a rigid rod, which, when given some initial lift from the vertical position, will swing back and forth under the influence of gravity over its central (lowest) point. ...Pendulum
A double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior. ...Double pendulum
For the novel Foucaults Pendulum by Umberto Eco, See Foucaults Pendulum (book). ...Foucault pendulum
A string instrument (also stringed instrument) is a musical instrument that produces sound by means of vibrating strings. ...String instruments
A vibration in a string is a wave. ...Vibrating string
Acoustics is a branch of physics and is the study of sound, mechanical waves in gases, liquids, and solids. ...Helmholtz resonator
Tacoma Narrows Bridge The Tacoma Narrows Bridge is a mile_long suspension bridge with a main span of 2800 ft (the 3rd largest in the world when it was first built) that carries Washington State Route 16 across the Tacoma Narrows of Puget Sound from Tacoma to Gig Harbor, Washington...Tacoma Narrows Bridge _ Galloping Gertie, an example of a self_exciting system
A tuning fork is a simple metal two_pronged fork with the tines formed from a U_shaped bar of elastic material (usually steel). ...Tuning fork

Electrical

The Armstrong Oscillator is named for Edwin Armstrong, its inventor. ...Armstrong oscillator
An astable multivibrator is an electronic circuit that has two states, neither one which is stable. ...Astable multivibrator
Clapp oscillator
A Colpitts oscillator, named after its inventor Edwin H. Colpitts, is one of a number of designs for electronic oscillator circuits. ...Colpitts oscillator
A crystal oscillator is an electronic device that uses the mechanical resonance of a physical crystal of piezoelectric material to create an electrical signal with a very precise frequency. ...Crystal oscillator
An electronic oscillator is an electronic circuit that produces a repetitive electronic signal, often a sine wave or a square wave. ...Electronic oscillator
Schematic Diagram The Hartley oscillator is an LC electronic oscillator that derives its feedback from a tapped coil and is varied in frequency by a variable capacitor. ...Hartley oscillator
A relaxation oscillator is an oscillator in which a capacitor is charged gradually and then discharged rapidly. ...Relaxation oscillator
An RLC circuit is a kind of electrical circuit composed of a resistor (R), an inductor (L), and a capacitor (C). ...RLC circuit
Vackar oscillator

Electro_mechanical

A microphone with a cord A microphone, sometimes called a mic (pronounced mike), is a device that converts sound into an electrical signal. ...Microphone
A loudspeaker is a device which converts an electrical signal into sound. ...Loudspeaker

Biological

The Lotka_Volterra equations, also known as the predator_prey equations, are a pair of first order, non_linear, differential equations frequently used to describe the dynamics of biological systems in which two species interact, one a predator and one its prey. ...Prey_predator systems

Human

Pilot_induced oscillations occur when the pilot of an aircraft inadvertently commands an often increasing series of corrections in opposite directions, each an attempt to correct for the previous overcorrection with an overcorrection in the opposite direction. ...Pilot_induced oscillation
Voice production is the generation of sound in the human speech organs. ...Voice production
Electroencephalography is the neurophysiologic exploration of the electrical activity of the brain by the application of electrodes to the scalp. ...Brain waves
" Good Vibrations is a song by The Beach Boys. ...Good Vibrations"

Economic and social

An abstract business cycle The business cycle or economic cycle refers to the ups and downs seen somewhat simultaneously in most parts of an economy. ...Business cycle
Publicly funded medicine is a level of medical service that is paid wholly or in majority part by public funds (taxes or quasi_taxes). ...Publicly funded medicine

The climate (ancient Greek: κλίμα) is the weather averaged over a long period of time. ...Climate and geophysics

The Chandler wobble is a small variation in Earths axis of rotation, discovered by American astronomer Seth Carlo Chandler in 1891. ...Chandler wobble
El Niño is also the nickname of Sergio García. ...El Niño_Southern Oscillation
The QBO (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 months. ...Quasi_biennial oscillation
This article is about tides in the ocean. ...Tides in the Earth, also known as the Earth or Terra, is the third planet outward from the Sun. ...Earth's Ocean (Okeanos, a Greek god of sea and water; Greek ωκεανός) covers almost three quarters (71%) of the surface of the Earth. ...oceans