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Related Concept Videos

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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Forced Oscillations01:06

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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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Damped Oscillations01:07

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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...
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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...
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Limits with Oscillating Discontinuities01:19

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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...
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RLC Circuit as a Damped Oscillator01:30

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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...
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Automatic Detection of Highly Organized Theta Oscillations in the Murine EEG
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On developing a framework for detection of oscillations in data.

Mohd Faheem Ullah1, Laya Das2, Sweta Parmar3

  • 1Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai, 600036, India.

ISA Transactions
|January 26, 2019
PubMed
Summary

This study introduces a novel framework for detecting oscillations in complex systems, addressing challenges like non-stationarity and noise. The new method proves robust and reliable across simulations and real-world climate and industrial data.

Keywords:
Intermittent oscillationsInterval halvingMulti-modal oscillations

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Area of Science:

  • Complex Systems Analysis
  • Signal Processing
  • Data Science

Background:

  • Oscillations are prevalent across diverse scientific domains, from physiology to climate science.
  • Existing oscillation detection methods struggle with complex data features like non-stationarity, intermittent signals, noise, and multimodal oscillations.
  • A unified framework is needed to effectively analyze such challenging oscillatory data.

Purpose of the Study:

  • To propose a novel, unified framework for robust oscillation detection.
  • To accommodate complex data characteristics including non-stationarity, intermittent oscillations, measurement noise, and multimodal oscillations.
  • To provide a reliable tool for analyzing oscillatory phenomena in various scientific and industrial applications.

Main Methods:

  • Development of a new analytical framework designed to handle non-stationary and noisy data.
  • Extensive simulation studies to rigorously test the framework's performance and reliability.
  • Application and validation of the framework on real-world datasets from climate science and industrial processes.

Main Results:

  • The proposed framework demonstrates high robustness and reliability in detecting oscillations.
  • The technique effectively handles data with non-stationarity, intermittent oscillations, measurement noise, and multimodal characteristics.
  • Successful application to diverse real-world datasets, validating its practical utility.

Conclusions:

  • The developed framework offers a significant advancement in oscillation detection methodologies.
  • It provides a reliable and versatile tool for analyzing complex oscillatory systems.
  • The framework's applicability across scientific and industrial fields highlights its broad potential impact.