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Related Concept Videos

Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
Damped Oscillations01:07

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...
Forced Oscillations01:06

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 Damping01:20

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...
Stability01:28

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Concept of Resonance and its Characteristics01:19

Concept of Resonance and its Characteristics

If a driven oscillator needs to resonate at a specific frequency, then very light damping is required. An example of light damping includes playing piano strings and many other musical instruments. Conversely, to achieve small-amplitude oscillations as in a car's suspension system, heavy damping is required. Heavy damping reduces the amplitude, but the tradeoff is that the system responds at more frequencies. Speed bumps and gravel roads prove that even a car's suspension system is not immune...

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Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
12:21

Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators

Published on: April 4, 2016

Stochastic resonance in coupled underdamped bistable systems.

A Kenfack1, Kamal P Singh

  • 1Physikalische und Theoretische Chemie, Freie University in Berlin, Takustr 3, 14195 Berlin, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary

We investigated stochastic resonance (SR) in coupled bistable systems. Optimal SR control was achieved by tuning damping and coupling, and using phase differences in driving forces.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Complex Systems

Background:

  • Stochastic Resonance (SR) is a phenomenon where a weak signal can be amplified by adding noise.
  • Bistable systems are often used to study SR, but understanding coupled systems is complex.
  • Inertia and coupling significantly influence SR dynamics in driven systems.

Purpose of the Study:

  • To investigate the onset and control of stochastic resonance (SR) in two mutually coupled, driven bistable systems.
  • To analyze the effects of inertia, coupling, and independent noises on SR.
  • To propose a method for controlling SR in these coupled systems.

Main Methods:

  • Analysis of two driven bistable systems subjected to independent noises.
  • Examination of the influence of inertia and coupling parameters.
  • Investigation of system behavior under varying coupling strengths, including weak and strong coupling.
  • Introduction of a phase difference between driving forces for control.

Main Results:

  • In uncoupled systems, critical damping parameters were identified for SR onset and optimization.
  • Weak coupling leads to SR emergence governed by chaos.
  • Strong coupling induces coherence but not synchronization.
  • An optimal coupling parameter was found to maximize SR in each subsystem.
  • A control scheme using phase differences in driving forces was proposed.

Conclusions:

  • Coupling significantly alters SR dynamics, with chaos playing a role in weakly coupled systems.
  • Coherence can be induced in strongly coupled systems, but synchronization does not occur.
  • SR in coupled bistable systems can be effectively controlled by manipulating driving forces and coupling parameters.