Oscillator

Oscillation is the Periodic variation, typically in Time , of some measure as seen, for example, in a swinging Pendulum . It is also known as periodic force. 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 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 "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 .

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 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 Mode s.

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 Wave s that have the characteristic that they can propagate.

NEURAL SYSTEMS

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.

EXAMPLES

See also: List Of Wave Topics

Mechanical