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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.
Oscillations are the origin of the sensation of musical tone.
Simple systems
The simplest 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 inertia which keeps it moving
beyond that position, establishing a new restoring force, now in the opposite sense. 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 sytem,
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 "inertia" that maintains motion; and
- Exchange in "energy" between that associated with "inertia" and that of 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.
Damped, driven and self-excited oscillations
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.
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, or random. In general, the response of the system is not independent of the 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 resonance.
Self-exciting systems
Some systems are able to extract energy from their 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 phenomenon of hunting is a
self-exciting oscillation in non-linear electrical circuits.
Coupled oscillations
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 respsective 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.
Continuous systems - waves
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.
Examples
See also: list of wave topics
Mechanical
Electrical
Electro-mechanical
Biological
Human
- Pilot-induced oscillation
- Voice production
Economic and social
Climate and geophysics
See also: Dynamical system | Feedback | Instability | Oscillation (mathematics) | Periodic function | Signal generator | Strange attractor |
Tuned mass damper | Vibrator
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