# Oscillatory Systems

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Oscillatory Systems

physical systems in which natural oscillation caused by the properties of the system itself arises as a result of disruption of the state of equilibrium.

From the standpoint of energy, oscillatory systems are divided into conservative systems, in which there are no energy losses or, more accurately, which may, with sufficient accuracy, be considered to lack such losses (mechanical systems without friction and without the radiation of elastic waves; electromagnetic systems without resistance and without the radiation of electromagnetic waves); dissipative systems, in which the energy originally imparted does not remain constant in the process of the oscillations but is expanded on work, as a result of which the oscillations attenuate; and self-oscillating systems, in which not only energy losses but also the addition of energy from constant energy sources in the system take place.

The parameters of oscillating systems (such as their mass, capacitance, and elasticity) usually depend on the processes taking place in them. Such oscillation systems are described by nonlinear equations and are classified as nonlinear systems. Oscillatory systems whose parameters may, with sufficient accuracy, be considered independent of the processes taking place in them and may be described by linear equations are called linear. The possibility of using the superposition principle is the main feature of linear oscillatory systems; this makes possible representation of the oscillations in a system as the sum of oscillations of a certain type.

Oscillatory systems are also distinguished according to the number of degrees of freedom—that is, the number of independent parameters (the generalized coordinates that define the state of the system). If the number N of such parameters is finite, the oscillatory systems are called discrete systems with N degrees of freedom. When N → ∞, distributed oscillatory systems (such as a string, diaphragm, electrical cable, or continuous solid system) are the limiting case. The general properties of oscillatory systems and the general mechanisms of the processes that take place in them are the subject of oscillation theory.

References in periodicals archive ?
Vibrations control is performed by changing the viscoplasticity of the working fluid in the damper channel for oscillatory systems containing both elastic elements and dampers.
LUBICH, Modulated Fourier expansions for continuous and discrete oscillatory systems, in Foundations of Computational Mathematics, Budapest 2011, F.
But even more significant, the new system theoretically proved that a connection existed between graph coloring and the natural dynamics of coupled oscillatory systems.
For higher order and/or oscillatory systems with complex dynamics, this operation can be quite difficult and time-consuming.
In this paper, we propose a BHTRKNM which is of order 3 and its application is extended to solving oscillatory systems, PDEs, and Hamiltonian systems including the energy conserving equation.
Simulations of Oscillatory Systems: With Award-Winning Software, Physics of Oscillations (online access included)
Symmetric and symplectic methods have been shown to have excellent numerical behavior in the long-term integration of oscillatory systems even if they are not Hamiltonian systems.
It would be of interest to search for this phenomenon not only in chemical or metabolic oscillatory systems but also in the many rhythmic processes occurring in the brain, which arise precisely from multiple regulatory interactions between neurons.
There are many approaches for approximating solutions to nonlinear oscillatory systems. The most widely studied approximation methods are the perturbation methods [24].
Underdamped systems, sometimes called oscillatory systems, are illustrated in Fig.

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