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Forced Oscillations

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.

Oscillations In An LC Circuit

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

Modes of Standing Waves - I

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...

Types of Damping

Types of Damping

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...

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...

Modes of Standing Waves: II

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....

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Related Experiment Video

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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

Diffusion-induced periodic transition between oscillatory modes in amplitude-modulated patterns.

Xiaodong Tang¹, Yuxiu He¹, Irving R Epstein²

¹College of Chemical Engineering, China University of Mining and Technology, Xuzhou 221008, China.

Chaos (Woodbury, N.Y.)

|July 3, 2014

Summary

Researchers discovered new transition zones in reaction-diffusion models, leading to complex amplitude-modulated waves. These findings reveal periodic pattern transitions and offer insights into wave stability using spatial recurrence rates.

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Area of Science:

Complex systems dynamics
Nonlinear phenomena in reaction-diffusion systems

Background:

Reaction-diffusion models exhibit complex spatiotemporal patterns.
Understanding wave packet dynamics and spiral waves is crucial in various scientific fields.

Purpose of the Study:

Investigate amplitude-modulated waves in a three-variable reaction-diffusion model.
Identify novel patterns and transition zones under mixed-mode oscillatory conditions.

Main Methods:

Simulations of a three-variable reaction-diffusion model.
Analysis of wave packets in 1D and target spirals/superspirals in 2D.
Characterization of pattern transitions and stability using spatial recurrence rates.

Main Results:

Discovery of new transition zones not present in homogeneous systems.
Observation of periodic transitions between local 1(N-1) and 1(N) oscillations.
Formation of amplitude-modulated complex patterns from transitions between (N-1)-armed and N-armed waves.

Conclusions:

Mixed-mode oscillations induce novel complex wave patterns.
Spatial recurrence rates are effective indicators for the stability of modulated patterns.
The study expands the understanding of pattern formation in reaction-diffusion systems.