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Oscillation of a sequence (shown in blue) is the difference between the limit superior and limit inferior of the sequence. In mathematics, the oscillation of a function or a sequence is a number that quantifies how much that sequence or function varies between its extreme values as it approaches infinity or a point.
Oscillation theory was initiated by Jacques Charles François Sturm in his investigations of Sturm–Liouville problems from 1836. There he showed that the n'th eigenfunction of a Sturm–Liouville problem has precisely n-1 roots.
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 ...
In mathematics, in the field of ordinary differential equations, the Sturm–Picone comparison theorem, named after Jacques Charles François Sturm and Mauro Picone, is a classical theorem which provides criteria for the oscillation and non-oscillation of solutions of certain linear differential equations in the real domain.
In mathematics, more specifically in dynamical systems, the method of averaging (also called averaging theory) exploits systems containing time-scales separation: a fast oscillation versus a slow drift. It suggests that we perform an averaging over a given amount of time in order to iron out the fast oscillations and observe the qualitative ...
A familiar example of parametric oscillation is "pumping" on a playground swing. [ 4 ] [ 5 ] [ 6 ] A person on a moving swing can increase the amplitude of the swing's oscillations without any external drive force (pushes) being applied, by changing the moment of inertia of the swing by rocking back and forth ("pumping") or alternately standing ...