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Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

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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
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Design Example: Underdamped Parallel RLC Circuit01:17

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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.
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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.
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Related Experiment Video

Updated: Dec 25, 2025

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
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The Goodwin Oscillator and its Legacy.

Didier Gonze1, Peter Ruoff2

  • 1Unité de Chronobiologie Théorique, Service de Chimie Physique CP 231, Université Libre de Bruxelles, Bvd du Triomphe, 1050, Brussels, Belgium. dgonze@ulb.ac.be.

Acta Biotheoretica
|March 27, 2020
PubMed
Summary

Brian Goodwin

Area of Science:

  • Biochemistry
  • Mathematical Biology
  • Systems Biology

Background:

  • Brian Goodwin's 1960s mathematical models demonstrated feedback inhibition's role in cellular oscillations.
  • His work explored the complex dynamics arising from coupled biochemical oscillators.
  • Goodwin's foundational research inspired subsequent theoretical investigations into biological oscillator mechanisms.

Purpose of the Study:

  • To summarize key ideas and findings from Brian Goodwin's pioneering work on biological oscillations.
  • To review theoretical modeling studies influenced by Goodwin's contributions.
  • To highlight the significance of Goodwin's models in understanding cellular and circadian clocks.

Main Methods:

  • Review of historical mathematical models of biological feedback inhibition.
Keywords:
Circadian rhythmsFeedback inhibitionGoodwin modelLimit cycle oscillations

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  • Analysis of theoretical investigations inspired by Goodwin's oscillator models.
  • Synthesis of findings related to minimal mechanisms for limit cycle oscillations.

    • Main Results:

    • Goodwin's models established feedback inhibition as a source of cellular oscillations.
    • Coupling of biochemical oscillators can generate rich and complex dynamics.
    • The adapted three-variable Goodwin model serves as a fundamental framework for various biological clocks.

    Conclusions:

    • Brian Goodwin's work laid the groundwork for understanding biological oscillations through mathematical modeling.
    • His research continues to influence the study of cellular rhythms, from ultradian to circadian processes.
    • The principles derived from Goodwin's models are crucial for deciphering the design of biological oscillators.