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Related Concept Videos

Damped Oscillations01:07

Damped Oscillations

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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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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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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.
Starting with a fixed...
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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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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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Magnetic Damping01:17

Magnetic Damping

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Eddy currents can produce significant drag on motion, called magnetic damping. For instance, when a metallic pendulum bob swings between the poles of a strong magnet, significant drag acts on the bob as it enters and leaves the field, quickly damping the motion.
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Fabrication and Testing of Microfluidic Optomechanical Oscillators
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Noisy oscillator: Random mass and random damping.

Stanislav Burov1, Moshe Gitterman1

  • 1Physics Department, Bar-Ilan University, Ramat Gan 52900, Israel.

Physical Review. E
|December 15, 2016
PubMed
Summary

This study explores a noisy oscillator with random mass and damping. Findings reveal how noise influences energy dynamics and stability, impacting stochastic resonance phenomena.

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • Linear damped noisy oscillators are fundamental in physics.
  • Understanding noise effects on system dynamics is crucial.
  • Multiplicative noise sources introduce complexities like random mass and damping.

Purpose of the Study:

  • To analyze a linear damped noisy oscillator subjected to two multiplicative noise sources.
  • To investigate the impact of random mass and damping on oscillator behavior.
  • To examine mean and energetic stabilities and the phenomenon of stochastic resonance.

Main Methods:

  • Derivation of general formulas for the first two moments of the oscillator's state.
  • Analysis of additive noise and noise in damping for energy influx and dissipation.

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  • Mathematical modeling of random mass effects due to molecule adhesion.
  • Investigation of stochastic resonance under separate and joint noise actions.

    • Main Results:

    • Formulas for the first two moments of the noisy oscillator are derived.
    • Additive and damping noise contribute to energy exchange with the environment.
    • Random mass significantly alters oscillator dynamics.
    • Conditions for mean and energetic stability are addressed.
    • Stochastic resonance is analyzed for individual and combined noise sources.

    Conclusions:

    • The study provides a comprehensive framework for understanding noisy oscillators with complex noise characteristics.
    • Noise plays a dual role, potentially destabilizing but also enabling phenomena like stochastic resonance.
    • The findings are relevant for systems where mass and damping can fluctuate randomly.