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Damped Oscillations

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...

Oscillations about an Equilibrium Position

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Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...

Types of Damping

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If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...

Forced Oscillations

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When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.

Limits with Oscillating Discontinuities

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An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the most...

Turbulent Flow

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Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent spots,...

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Related Experiment Video

Updated: May 9, 2026

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Published on: May 9, 2021

Oscillations in a turbulence-condensate system.

Pearson Miller¹, Natalia Vladimirova, Gregory Falkovich

¹Yale University, Department of Physics, New Haven, Connecticut 06511, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 16, 2013

Summary

Developed turbulence in the Gross-Pitaevsky model exhibits periodic oscillations. These oscillations arise from condensate-imposed phase coherence and anomalous correlations, not predator-prey dynamics.

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Magnetically Induced Rotating Rayleigh-Taylor Instability

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Area of Science:

Fluid dynamics
Quantum turbulence
Nonlinear physics

Background:

Developed turbulence in the Gross-Pitaevsky model features an inverse cascade leading to condensate formation.
The turbulent system exhibits persistent periodic oscillations around a steady state.

Purpose of the Study:

To investigate the underlying mechanism of nondecaying periodic oscillations in turbulent Gross-Pitaevsky systems.
To challenge the previously suggested predator-prey model for these oscillations.

Main Methods:

Analysis of developed turbulence within the Gross-Pitaevsky equation.
Investigation of wave-exchange dynamics between turbulence and condensate.
Examination of phase coherence and anomalous correlations.

Main Results:

The system displays periodic oscillations due to a dynamic exchange between turbulence and condensate.
These oscillations are demonstrated to be independent of predator-prey interactions.
Phase coherence and anomalous correlations imposed by the condensate are identified as the cause.

Conclusions:

Collective oscillations in this turbulent system are driven by condensate properties.
The findings refine the understanding of quantum turbulence and condensate dynamics.