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Related Concept Videos

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...
Sound Waves: Resonance01:14

Sound Waves: Resonance

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...
Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

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
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.
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

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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Coupling-induced resonance in two mutually and asymmetrically coupled oscillators.

Thomas W Carr1

  • 1Department of Mathematics, Southern Methodist University, Dallas, Texas 75275-0156, USA. tcarr@smu.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
PubMed
Summary

We found that controlling coupling in oscillators can induce resonance, leading to large amplitudes. This effect is observable in systems where amplitude is key, unlike phase-only models.

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Area of Science:

  • Nonlinear dynamics
  • Physics of coupled systems

Background:

  • Coupled oscillators are fundamental in many scientific fields.
  • Understanding resonance phenomena is crucial for analyzing oscillator behavior.

Purpose of the Study:

  • To investigate coupling-induced resonance in mutually coupled oscillators.
  • To explore the influence of nonlinear dissipation and frequency corrections on this resonance.
  • To analyze the effects of delayed coupling on bifurcation dynamics and multistability.

Main Methods:

  • Analysis of two mutually coupled oscillators with independent control over coupling parameters (magnitude, sign, delay).
  • Investigation of nonlinear dissipation and amplitude-dependent frequency correction effects.
  • Tracking of resonant bifurcation equations under delayed coupling, including imperfect bifurcations and isola generation.

Main Results:

  • Identified a coupling-induced resonance leading to large oscillation amplitudes.
  • Demonstrated that nonlinear dissipation and frequency corrections impact the coupling resonance.
  • Observed the generation of multistability intervals through imperfect bifurcations and isolas with delayed coupling.

Conclusions:

  • Coupling-induced resonance is a significant phenomenon in coupled oscillators.
  • Delayed coupling can lead to complex dynamics, including multistability.
  • The findings are relevant for systems where oscillation amplitude is a critical variable.