Oscillation

Oscillation is the repetitive or periodic variation, typically in time, 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 and alternating current. 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 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. The term vibration is precisely used to describe a mechanical oscillation.

Oscillation, especially rapid oscillation, may be an undesirable phenomenon in process control and control theory (e.g. in sliding mode control), where the aim is convergence to stable state. In these cases it is called chattering or flapping, as in valve chatter, and route flapping.

Simple harmonic oscillation

Main article: Simple harmonic motion

Imagine a weight attached to a spring. When the spring is not stretched or squeezed, the weight stays still — this is its balanced position. If you move the weight away from this balance point, the spring pulls it back. But once the weight starts moving back, it keeps going past the balance point because it has speed. This makes it swing back and forth.

This kind of back-and-forth movement happens because the spring gets stronger at pulling back the further you stretch it. The time it takes for one full swing back and forth is called the period. The weight moves between two points, turning its speed into stored energy in the spring and back again.

Two-dimensional oscillators

In two or three dimensions, things that swing back and forth, like a pendulum, work in a similar way to one dimension. The simplest example is when the force pulling something back to its starting point is the same in all directions. This creates a pattern where the movement can be described using different equations for each direction.

With oscillators that have different forces in different directions, the patterns can change. For example, if one direction swings twice as fast as another, it can make a figure-eight shape. If the speeds are not simple ratios, the motion will never exactly repeat.

Damped oscillations

Main article: Harmonic oscillator

See also: Anti-vibration compound

In real life, things that swing or move back and forth lose energy over time. This happens because of forces like friction or resistance, which turn some of the energy into heat. Because of this, the movement gets smaller and smaller unless something adds more energy.

When a force that slows things down is added, it changes how the movement works. This can be shown with math, where a special equation describes how the movement changes. There are three ways this can happen: the movement slows down a little, a lot, or just the right amount.

Driven oscillations

An oscillating system can also be influenced by an external force. For example, when an electrical circuit is connected to a power source, the oscillation is called driven.

A simple example is a spring and mass system with a smooth, repeating driving force. In some cases, energy from the surroundings can cause a system to oscillate. For instance, in air travel, a small shift in an airplane wing can lead to changes in how air flows over it, causing further shifts. Eventually, the wing's own strength brings it back, allowing it to swing back and forth.

Resonance

Resonance happens in a system when the frequency at which it is being driven matches its natural frequency. At this point, the swings or oscillations become the strongest.

Coupled oscillations

See also: Injection locking

When systems have more than one part that can move, their movements can affect each other. This is called coupling. For example, two pendulum clocks hanging on the same wall will often swing together. This was first seen by Christiaan Huygens in 1665.

One simple example is two weights connected by springs. Depending on how you start the weights moving, they can swing in different ways. Sometimes they move together, and sometimes they move in opposite directions. There are also special cases where energy moves between two kinds of swinging, like in a Wilberforce pendulum where the object swings up and down and also spins around.

Coupled oscillators describe how two related things can influence each other. Sometimes they end up moving together at a middle speed. Other times, one moving thing can affect another without being changed itself, leading to interesting patterns.

Small oscillation approximation

In physics, when a system has a balance point and steady forces, we can think of it as moving back and forth in a simple way close to that balance point. This helps us understand more complex actions, like how atoms interact.

One example uses something called the Lennard-Jones potential to show how this works. By studying the balance point and how the system changes around it, we can find out how often these back-and-forth movements happen. This idea is useful for understanding many natural patterns, including how planets move around the sun.

Continuous system – waves

Main article: Wave

When a system has many parts moving together, like a string or the surface of water, it can create waves. These waves move through the system and show how the parts are connected and moving over time.

Mathematics

In math, oscillation looks at how much a sequence or function moves between its highest and lowest points. We study this for sequences of numbers, for functions at a single point, and for functions over a range.

Examples

Mechanical

Some everyday examples of oscillation include:

• 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
• Phugoid oscillation
• Hunting oscillation

Electrical

Main article: Electronic oscillator

Electrical oscillations include:

• 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)
• Oscillator Toda or self-pulsation (pulsation of output power of laser at frequencies 10⁴ Hz – 10⁶ Hz in the transient regime)
• Quantum oscillator may refer to an optical local oscillator, as well as to a usual model in quantum optics.

Biological

• Circadian rhythm
• Bacterial Circadian Rhythms
• Circadian oscillator
• Lotka–Volterra equation
• Neural oscillation
• Oscillating gene
• Segmentation clock

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