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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

Design Example: Underdamped Parallel RLC Circuit

Design Example: Underdamped Parallel RLC Circuit

Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...

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...

RLC Circuit as a Damped Oscillator

RLC Circuit as a Damped Oscillator

An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...

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.

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...

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Updated: Jun 19, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Published on: December 15, 2021

Event-related desynchronization in diffusively coupled oscillator models.

Jane H Sheeba¹, V K Chandrasekar, M Lakshmanan

¹Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli-620 024, Tamilnadu, India.

Physical Review Letters

|October 2, 2009

Summary

This study explains event-related desynchronization (ERD) using nonlinear oscillator models. Sufficient event strength causes ERD, with task success depending on the desynchronized state, offering insights into brain function and physical systems.

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Area of Science:

Neuroscience
Complex Systems Theory
Nonlinear Dynamics

Background:

Event-related desynchronization (ERD) is a key neurophysiological phenomenon.
Understanding the mechanisms underlying ERD is crucial for cognitive neuroscience.

Purpose of the Study:

To provide a theoretical explanation for event-related desynchronization (ERD).
To explore the role of nonlinear dynamics in generating ERD.
To investigate the relationship between desynchronized states and task accomplishment.

Main Methods:

Modeling diffusively coupled nonlinear oscillators.
Numerical simulations of limit cycle and chaotic systems.
Analytical derivation of ERD emergence.

Main Results:

ERD emerges when the strength of an event exceeds a critical threshold.
The nature of the desynchronized state dictates the success of behavioral or functional tasks.
The phenomenon was demonstrated in both limit cycle and chaotic oscillator models.

Conclusions:

Diffusively coupled nonlinear oscillators provide a viable model for ERD.
ERD is a fundamental property of certain nonlinear dynamical systems.
The findings suggest potential applications beyond neuroscience, in other physical systems.