Oscillation

"Oscillator" redirects here. For other uses, see Oscillator (disambiguation).

An undamped spring–mass system is an oscillatory system

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. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.

Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy.

Contents

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  1 Simple harmonic
  


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  2 Damped and driven oscillations
  


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  3 Coupled oscillations
  


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  4 Continuous systems – waves
  


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  5 Mathematics
  


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  6 Examples
  
  
  
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    6.1 Mechanical
    
  
  
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    6.2 Electrical
    
  
  
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    6.3 Electro-mechanical
    
  
  
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    6.4 Optical
    
  
  
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    6.5 Biological
    
  
  
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    6.6 Human
    
  
  
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    6.7 Economic and social
    
  
  
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    6.8 Climate and geophysics
    
  
  
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    6.9 Astrophysics
    
  
  
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    6.10 Quantum mechanical
    
  
  
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    6.11 Chemical
    
  
  
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    6.12 Computing
    
  
  
  
  


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  7 See also
  


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  8 References
  


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  9 External links
  

Simple harmonic

Main article: Simple harmonic motion

The simplest mechanical oscillating system is a weight attached to a linear spring subject to only weight and tension. 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 which keeps it moving beyond that position, establishing a new restoring force in the opposite sense. If a constant force 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 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 and the regular periodic motion is known as simple harmonic motion. 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. 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

Main article: Harmonic oscillator

All real-world oscillator systems are thermodynamically irreversible. This means there are dissipative processes such as friction or electrical resistance 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.

See also: Anti-vibration compound

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.

Some systems can be excited by energy transfer from the environment. This transfer typically occurs where systems are embedded in some fluid flow. 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. At sufficiently large displacements, the stiffness of the wing dominates to provide the restoring force that enables an oscillation.

Coupled oscillations

Two pendulums with the same period fixed on a string act as pair of coupled oscillators. The oscillation alternates between the two.

Experimental Setup of Huygens synchronization of two clocks

The harmonic oscillator and the systems it models have a single degree 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 (of identical frequency) mounted on a common wall will tend to synchronise. This phenomenon was first observed by Christiaan Huygens in 1665.^[1] 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 modes.

More special cases are the coupled oscillators where energy alternates between two forms of oscillation. Well-known is the Wilberforce pendulum, 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

Main article: Wave

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. 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.

Mathematics

Main article: Mathematics of oscillation

Oscillation of a sequence (shown in blue) is the difference between the limit superior and limit inferior of the sequence.

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 of real numbers, oscillation of a real valued function at a point, and oscillation of a function on an interval (or open set).

Examples

Mechanical

• Double pendulum


• Foucault pendulum


• Helmholtz resonator


• Oscillations in the Sun (helioseismology), stars (asteroseismology) and Neutron-star oscillations.


• Quantum harmonic oscillator


• Playground swing


• String instruments


• Torsional vibration


• Tuning fork


• Vibrating string


• Wilberforce pendulum


• Lever escapement

Electrical

Main article: Electronic oscillator

• Alternating current


• Armstrong (or Tickler or Meissner) oscillator


• Astable multivibrator


• Blocking oscillator


• Butler oscillator


• Clapp oscillator


• Colpitts oscillator


• Delay-line oscillator


• Electronic oscillator


• Extended interaction oscillator


• Hartley oscillator


• Oscillistor


• Phase-shift oscillator


• Pierce oscillator


• Relaxation oscillator


• RLC circuit


• Royer oscillator


• Vačkář oscillator


• Wien bridge oscillator

Electro-mechanical

• Crystal oscillator

Optical

• 
  Laser (oscillation of electromagnetic field with frequency of order 10¹⁵ Hz)


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  Oscillator Toda or self-pulsation (pulsation of output power of laser at frequencies 10⁴ Hz – 10⁶ Hz in the transient regime)


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  Quantum oscillator may refer to an optical local oscillator, as well as to a usual model in quantum optics.

Biological

• Circadian rhythm


• Circadian oscillator


• Lotka–Volterra equation


• Neural oscillation


• Oscillating gene


• Segmentation oscillator

Human

• Neural oscillation


• Insulin release oscillations


• gonadotropin releasing hormone pulsations


• Pilot-induced oscillation


• Voice production

Economic and social

• Business cycle


• Generation gap


• 
  Malthusian 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 stars


• Cyclic Model

Quantum mechanical

• 
  Neutral particle oscillation, e.g. neutrino oscillations
  


• Quantum harmonic oscillator

Chemical

• Belousov–Zhabotinsky reaction


• Mercury beating heart


• Briggs–Rauscher reaction


• Bray–Liebhafsky reaction

Computing

• Cellular Automata oscillator

See also

• Antiresonance


• Beat (acoustics)


• BIBO stability


• Critical speed


• Cycle (music)


• Dynamical system


• Earthquake engineering


• Feedback


• Frequency


• Oscillator phase noise


• Periodic function


• Phase noise


• Reciprocating motion


• Resonator


• Rhythm


• Seasonality


• Self-oscillation


• Hidden oscillation


• Signal generator


• Squegging


• Strange attractor


• Structural stability


• Tuned mass damper


• Vibration


• Vibrator (mechanical)

References

1. 
   ^ Strogatz, Steven. Sync: The Emerging Science of Spontaneous Order. Hyperion, 2003, pp 106-109
   

External links

Look up oscillation in Wiktionary, the free dictionary.

• 
  Media related to Oscillation at Wikimedia Commons


• 
  Vibrations – a chapter from an online textbook

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