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Related Concept Videos

Concept of Resonance and its Characteristics01:19

Concept of Resonance and its Characteristics

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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...
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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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Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
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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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Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
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Second Order systems II01:18

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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.
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Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
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Vibrational and stochastic resonances in driven nonlinear systems: part 2.

U E Vincent1,2, P V E McClintock2, I A Khovanov3

  • 1Department of Physical Sciences, Redeemer's University, P.M.B. 230, Ede, Nigeria.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|April 12, 2021
PubMed
Summary

Nonlinear systems exhibit resonance phenomena when driven by external forces. This research explores advanced applications of vibrational resonance and stochastic resonance in diverse technologies.

Keywords:
driven oscillatorsnonlinear systemsstochastic resonancevibrational resonance

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Area of Science:

  • Physics
  • Engineering
  • Applied Mathematics

Background:

  • Nonlinearity is a fundamental characteristic of many natural and engineered systems.
  • The study of nonlinear dynamics is crucial due to the widespread occurrence of nonlinear phenomena across scientific disciplines.
  • Resonance is a key phenomenon in driven nonlinear systems, with vibrational and stochastic resonance being notable examples.

Purpose of the Study:

  • To provide an overview of vibrational and stochastic resonances in driven nonlinear systems.
  • To discuss state-of-the-art technologies leveraging these resonance phenomena.
  • To highlight advancements not covered in previous related works.

Main Methods:

  • The article discusses theoretical concepts and experimental applications of nonlinear dynamics.
  • It reviews recent technological advancements and their underlying principles.
  • Focus is placed on phenomena arising from external harmonic or stochastic excitation.

Main Results:

  • Vibrational resonance and stochastic resonance can be induced in nonlinear systems through external driving forces.
  • These resonance phenomena have practical applications in improving image quality.
  • They are also applied in designing vibration-exerting devices, energy harvesting, and controlling aerodynamic instabilities.

Conclusions:

  • Vibrational and stochastic resonances are significant phenomena in driven nonlinear systems with broad technological implications.
  • The discussed technologies represent promising applications of nonlinear dynamics.
  • This work contributes to a comprehensive understanding of resonance in nonlinear systems.