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Related Concept Videos

Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
Forced Oscillations01:06

Forced Oscillations

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.
Damped Oscillations01:07

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 Position01:04

Oscillations about an Equilibrium Position

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...
Modes of Standing Waves: II01:04

Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end.
Modes of Standing Waves - I01:03

Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This phenomenon...

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Related Experiment Video

Updated: Jul 6, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Published on: June 8, 2018

Introduction to focus issue: mixed mode oscillations: experiment, computation, and analysis.

Morten Brons1, Tasso J Kaper, Horacio G Rotstein

  • 1Department of Mathematics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark.

Chaos (Woodbury, N.Y.)
|April 2, 2008
PubMed
Summary

Mixed mode oscillations (MMOs) are dynamic system behaviors switching between fast/slow and small/large amplitudes. This collection explores MMOs across physical, chemical, and biological systems.

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Area of Science:

  • Dynamical Systems and Nonlinear Science
  • Complex Systems Dynamics

Background:

  • Mixed mode oscillations (MMOs) are characterized by the coexistence of multiple types of periodic orbits within a dynamical system.
  • These oscillations involve transitions between distinct behaviors, such as fast and slow dynamics or small and large amplitude motions.

Discussion:

  • This focus issue compiles research on the theoretical, numerical, and experimental investigation of MMOs.
  • The articles cover a broad spectrum of applications, highlighting the ubiquity of MMOs in natural phenomena.

Key Insights:

  • MMOs represent a fundamental mode of behavior in diverse natural systems, ranging from simple to complex forms.
  • Understanding MMOs is crucial for modeling and predicting the behavior of various physical, chemical, and biological processes.

Outlook:

  • Future research will likely focus on developing more sophisticated analytical tools and computational methods for MMO analysis.
  • Exploring novel applications of MMOs in emerging fields such as neuroscience and materials science is anticipated.