Oscillation
:''For other uses, see
oscillator (disambiguation)Oscillation is the
periodic variation, typically in
time, of some measure as seen, for example, in a swinging
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
biological systems and in human
society.
The simplest mechanical oscillating system is a
mass, subject to the
force of
gravity, attached to a
linear spring. The system is in an
equilibrium state when the
weight of the mass is balanced by the
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
momentum which keeps it moving beyond that position,
establishing a new restoring force, now in the opposite sense and this time due to gravity.
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 the spring-mass system, oscillations occur because, when at the
static equilibrium displacement, the mass has
kinetic energy which is converted into
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 "momentum" or kinetic energy that maintains motion; and
*Exchange in "energy" between that kinetic and potential energy due to the restoring force.
The
harmonic oscillator offers a model of many more complicated types of oscillation and can be extended by the use of
Fourier analysis.
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. 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.
Self inducing oscillations
Some systems can be excited by energy transfer from the environment. This 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 greater displacement before, at sufficiently large displacements, the
stiffness of the wing dominates to provide the restoring force that enables an oscillation.
The harmonic oscillator, and the more complicated systems for which it stands as a simple model, has a single
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.
As the number of degrees of freedom becomes indefinitely large, a system approaches
continuity, for example, a string or the surface of a body of
water. Such systems have an
infinite number of normal modes and their oscillations occur in the form of
waves that have the characteristic that they can propagate.
Neural oscillations occur in individual cells and cell ensembles. Depending on the frequency, brain area and behavior associated with neuronal oscillations, a diversity of functions have been suggested.
See also:
list of wave topicsMechanical
*
Pendulum*
Double pendulum*
Foucault pendulum*
String instruments
*
Vibrating string*
Helmholtz resonator*
Tacoma Narrows Bridge -
Galloping Gertie, an example of a high Q system
*
Tuning fork*
Playground swingElectrical
*
Armstrong oscillator *
Astable multivibrator*
Blocking oscillator*
Clapp oscillator*
Colpitts oscillator*
Crystal oscillator*
Electronic oscillator*
Hartley oscillator*
Relaxation oscillator*
RLC circuit*
Wien bridge oscillator*
Royer oscillator*
Vačkář oscillatorElectro-mechanical
*
Microphone*
LoudspeakerBiological
*
Prey-predator systemsHuman
*
Pilot-induced oscillation*
Voice production*
Brain waves*"
Good vibrations"
Economic and social
*
Business cycleClimate and geophysics
*
Chandler wobble*
El Niño-Southern Oscillation*
Quasi-biennial oscillation*
Tides in the
Earth's
oceans
*
Dynamical system*
Feedback*
Stability*
Oscillation (mathematics)*
Self oscillation*
Periodic function*
Signal generator*
Strange attractor*
Tuned mass damper*
Vibrator*
Rhythm*
Circadian rhythm*
Time period*
Pendulum*
Vibrations - a chapter from an online textbook
.
