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oscillation
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http://en.wikipedia.org/wiki/Oscillation 1/5
Anundampedspringmasssystemisanoscillatorysystem
OscillationFromWikipedia,thefreeencyclopedia
Oscillationistherepetitivevariation,typicallyintime,ofsomemeasureaboutacentralvalue(oftenapointofequilibrium)orbetweentwoormoredifferentstates.Familiarexamplesincludeaswingingpendulumandalternatingcurrentpower.Thetermvibrationissometimesusedmorenarrowlytomeanamechanicaloscillationbutissometimesusedasasynonymof"oscillation".
Oscillationsoccurnotonlyinmechanicalsystemsbutalsoindynamicsystemsinvirtuallyeveryareaofscience:forexamplethebeatinghumanheart,businesscyclesineconomics,predatorpreypopulationcyclesinecology,geothermalgeysersingeology,vibratingstringsinmusicalinstruments,periodicfiringofnervecellsinthebrain,andtheperiodicswellingofCepheidvariablestarsinastronomy.
Contents
1Simpleharmonicoscillator2Dampedanddrivenoscillations3Coupledoscillations4Continuoussystemswaves5Mathematics6Examples
6.1Mechanical6.2Electrical6.3Electromechanical6.4Optical6.5Biological6.6Human6.7Economicandsocial6.8Climateandgeophysics6.9Astrophysics6.10Quantummechanical6.11Chemical
7Seealso8References9Externallinks
Simpleharmonicoscillator
http://en.wikipedia.org/wiki/Oscillation 2/5
Thesimplestmechanicaloscillatingsystemisamassattachedtoalinearspringsubjecttoonlyweightandtension.Suchasystemmaybeapproximatedonanairtableoricesurface.Thesystemisinanequilibriumstatewhenthespringisstatic.Ifthesystemisdisplacedfromtheequilibrium,thereisanetrestoringforceonthemass,tendingtobringitbacktoequilibrium.However,inmovingthemassbacktotheequilibriumposition,ithasacquiredmomentumwhichkeepsitmovingbeyondthatposition,establishinganewrestoringforceintheoppositesense.Ifaconstantforcesuchasgravityisaddedtothesystem,thepointofequilibriumisshifted.Thetimetakenforanoscillationtooccurisoftenreferredtoastheoscillatoryperiod.
Systemswheretherestoringforceonabodyisdirectlyproportionaltoitsdisplacement,suchasthedynamicsofthespringmasssystem,aredescribedmathematicallybythesimpleharmonicoscillatorandtheregularperiodicmotionisknownassimpleharmonicmotion.Inthespringmasssystem,oscillationsoccurbecause,atthestaticequilibriumdisplacement,themasshaskineticenergywhichisconvertedintopotentialenergystoredinthespringattheextremesofitspath.Thespringmasssystemillustratessomecommonfeaturesofoscillation,namelytheexistenceofanequilibriumandthepresenceofarestoringforcewhichgrowsstrongerthefurtherthesystemdeviatesfromequilibrium.
Dampedanddrivenoscillations
Allrealworldoscillatorsystemsarethermodynamicallyirreversible.Thismeanstherearedissipativeprocessessuchasfrictionorelectricalresistancewhichcontinuallyconvertsomeoftheenergystoredintheoscillatorintoheatintheenvironment.Thisiscalleddamping.Thus,oscillationstendtodecaywithtimeunlessthereissomenetsourceofenergyintothesystem.Thesimplestdescriptionofthisdecayprocesscanbeillustratedbyoscillationdecayoftheharmonicoscillator.
Inaddition,anoscillatingsystemmaybesubjecttosomeexternalforce,aswhenanACcircuitisconnectedtoanoutsidepowersource.Inthiscasetheoscillationissaidtobedriven.
Somesystemscanbeexcitedbyenergytransferfromtheenvironment.Thistransfertypicallyoccurswheresystemsareembeddedinsomefluidflow.Forexample,thephenomenonofflutterinaerodynamicsoccurswhenanarbitrarilysmalldisplacementofanaircraftwing(fromitsequilibrium)resultsinanincreaseintheangleofattackofthewingontheairflowandaconsequentialincreaseinliftcoefficient,leadingtoastillgreaterdisplacement.Atsufficientlylargedisplacements,thestiffnessofthewingdominatestoprovidetherestoringforcethatenablesanoscillation.
Coupledoscillations
Theharmonicoscillatorandthesystemsitmodelshaveasingledegreeoffreedom.Morecomplicatedsystemshavemoredegreesoffreedom,forexampletwomassesandthreesprings(eachmassbeingattachedtofixedpointsandtoeachother).Insuchcases,thebehaviorofeachvariableinfluencesthatoftheothers.Thisleadstoacouplingoftheoscillationsoftheindividualdegreesoffreedom.Forexample,twopendulumclocks(ofidenticalfrequency)mountedonacommonwallwilltendtosynchronise.ThisphenomenonwasfirstobservedbyChristiaanHuygensin1665.[1]Theapparentmotionsofthecompoundoscillationstypicallyappearsverycomplicatedbutamoreeconomic,computationallysimplerandconceptuallydeeperdescriptionisgivenbyresolvingthemotionintonormalmodes.
Morespecialcasesarethecoupledoscillatorswhereenergyalternatesbetweentwoformsofoscillation.WellknownistheWilberforcependulum,wheretheoscillationalternatesbetweenanelongationofaverticalspringandtherotationofanobjectattheendofthatspring.
Continuoussystemswaves
http://en.wikipedia.org/wiki/Oscillation 3/5
Twopendulumswiththesameperiodfixedonastringactaspairofcoupledoscillators.Theoscillationalternatesbetweenthetwo.
Oscillationofasequence(showninblue)isthedifferencebetweenthelimitsuperiorandlimitinferiorofthesequence.
Asthenumberofdegreesoffreedombecomesarbitrarilylarge,asystemapproachescontinuityexamplesincludeastringorthesurfaceofabodyofwater.Suchsystemshave(intheclassicallimit)aninfinitenumberofnormalmodesandtheiroscillationsoccurintheformofwavesthatcancharacteristicallypropagate.
Mathematics
Themathematicsofoscillationdealswiththequantificationoftheamountthatasequenceorfunctiontendstomovebetweenextremes.Thereareseveralrelatednotions:oscillationofasequenceofrealnumbers,oscillationofarealvaluedfunctionatapoint,andoscillationofafunctiononaninterval(oropenset).
Examples
Mechanical
DoublependulumFoucaultpendulumHelmholtzresonatorOscillationsintheSun(helioseismology),stars(asteroseismology)andNeutronstaroscillations.QuantumharmonicoscillatorPlaygroundswing
Electromechanical
CrystaloscillatorLoudspeakerMicrophone
Optical
Laser(oscillationofelectromagneticfieldwith
frequencyoforder1015Hz)OscillatorTodaorselfpulsation(pulsationof
Economicandsocial
BusinesscycleGenerationgapMalthusianeconomicsNewscycle
Climateandgeophysics
AtlanticmultidecadaloscillationChandlerwobbleClimateoscillation
http://en.wikipedia.org/wiki/Oscillation 4/5
StringinstrumentsTorsionalvibrationTuningforkVibratingstringWilberforcependulumLeverescapement
Electrical
AlternatingcurrentArmstrong(orTicklerorMeissner)oscillatorAstablemultivibratorBlockingoscillatorButleroscillatorClapposcillatorColpittsoscillatorDelaylineoscillatorDow(orultraaudion)oscillatorElectronicoscillatorHartleyoscillatorOscillistorPierceoscillatorRelaxationoscillatorRLCcircuitRoyeroscillatorVakoscillatorWienbridgeoscillator
outputpoweroflaserat
frequencies104Hz
106Hzinthetransientregime)Quantumoscillatormayrefertoanopticallocaloscillator,aswellastoausualmodelinquantumoptics.
Biological
CircadianrhythmCircadianoscillatorLotkaVolterraequationNeuraloscillationOscillatinggeneSegmentationoscillator
Human
NeuraloscillationInsulinreleaseoscillationsgonadotropinreleasinghormonepulsationsPilotinducedoscillationVoiceproduction
ElNioSouthernOscillationPacificdecadaloscillationQuasibiennialoscillation
Astrophysics
NeutronstarsCyclicModel
Quantummechanical
NeutrinooscillationsQuantumharmonicoscillator
Chemical
BelousovZhabotinskyreactionMercurybeatingheartBriggsRauscherreactionBrayLiebhafskyreaction
Seealso
AntiresonanceBeat(acoustics)BIBOstabilityCriticalspeedCycle(music)DynamicalsystemEarthquakeengineering
OscillatorphasenoisePeriodicfunctionPhasenoiseReciprocatingmotionResonatorRhythmSeasonality
SignalgeneratorSqueggingStrangeattractorStructuralstabilityTunedmassdamperVibrationVibrator(mechanical)
http://en.wikipedia.org/wiki/Oscillation 5/5
FeedbackFrequency
SelfoscillationHiddenoscillation
References
1. ^Strogatz,Steven.Sync:TheEmergingScienceofSpontaneousOrder.Hyperion,2003,pp106109
Externallinks
Vibrations(http://www.lightandmatter.com/html_books/3vw/ch01/ch01.html)achapterfromanonlinetextbook
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Categories: Oscillation Earthquakeengineering
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