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Related Concept Videos

Types of Damping01:20

Types of Damping

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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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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.
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Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

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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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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.
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RLC Series Circuits01:30

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An RLC series circuit comprises an inductor, a resistor, and a charged capacitor connected in series. When the circuit is closed, the capacitor begins to discharge through the resistor and inductor by transferring energy from the electric field to the magnetic field. Here, the resistor connected to the circuit causes energy losses; therefore, on the complete discharge of the capacitor, the magnetic field energy acquired by the inductor is less than the original electric field energy of the...
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Forced Oscillations01:06

Forced Oscillations

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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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Time-delayed Duffing oscillator in an active bath.

Antonio A Valido1, Mattia Coccolo1, Miguel A F Sanjuán1

  • 1Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.

Physical Review. E
|January 20, 2024
PubMed
Summary
This summary is machine-generated.

Active particles, modeled by stochastic processes, exhibit complex dynamics in forced, time-delayed Duffing oscillators. Noise and time delay interplay to alter oscillation amplitude and frequency, revealing stochastic resonance effects.

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Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Active matter physics

Background:

  • Active particles are ubiquitous in natural and artificial systems.
  • Their dynamics are often modeled using stochastic processes with Gaussian white and Ornstein-Uhlenbeck noises.
  • Time-delayed systems introduce complex behaviors not seen in non-delayed counterparts.

Purpose of the Study:

  • Investigate the nonlinear dynamics of a forced, time-delayed Duffing oscillator under different noise types.
  • Analyze the impact of time delay, noise strength, and driving force on oscillation amplitude and frequency.
  • Explore the interplay between noise, forcing, and time delay in shaping system dynamics.

Main Methods:

  • Numerical simulation of the forced, time-delayed Duffing oscillator.
  • Analysis of steady-state oscillation amplitude and characteristic frequency.
  • Systematic variation of noise strength, driving force amplitude, and time delay values.

Main Results:

  • Time delay significantly modifies the system's response to noise compared to non-delayed systems.
  • Oscillation amplitude can increase with noise strength when time delay acts as damping.
  • Trajectories transition from periodic to aperiodic, influenced by the competition between noise and driving force.
  • Stochastic resonance can promote interwell motion under specific noise and forcing conditions.

Conclusions:

  • The interplay of noise, forcing, and time delay creates rich and complex dynamics in the Duffing oscillator.
  • Time delay's role is context-dependent, capable of both damping and sustaining oscillations.
  • Noise can either disrupt or restore regular motion, depending on the system parameters and time delay effects.