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Related Concept Videos

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...
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...
Parallel Resonance01:23

Parallel Resonance

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:
Resonance in an AC Circuit01:26

Resonance in an AC Circuit

The property of an inductor makes it resist any change in the current passing through it, while the property of a capacitor is to build up the charge across its terminals. Hence, if an inductor and capacitor are connected in series, they have opposite effects on the relative phase between current and voltage. The current through the circuit undergoes forced oscillation at the frequency of the source. The resistance term in an R-L-C circuit acts as a damping term because power is dissipated...
Characteristics of Series Resonant Circuit01:24

Characteristics of Series Resonant Circuit

Series resonance occurs in a circuit containing inductive (L), capacitive (C), and resistive (R) elements connected sequentially. At the resonance frequency, the inductive and capacitive reactances are equal in magnitude but opposite in sign, effectively canceling each other. This causes the circuit's impedance is minimal, primarily determined by the resistance R. The resonant frequency of an RLC circuit is defined as:
Series Resonance01:17

Series Resonance

The RLC circuit impedance is defined as the ratio of the supply voltage to the circuit current. Resonance in such a circuit occurs when the imaginary part of this impedance equals zero. This specific condition means that the inductive reactance is exactly equal to the capacitive reactance. The frequency at which this happens is known as the resonant frequency. Mathematically, the resonant frequency is inversely proportional to the square root of the product of the inductance (L) and capacitance...

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Slow passage through resonance.

Youngyong Park1, Younghae Do, Juan M Lopez

  • 1Department of Mathematics, Kyungpook National University, Daegu, South Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
PubMed
Summary
This summary is machine-generated.

Resonance onset in a damped oscillator occurs earlier than expected, at a specific "jump frequency." This phenomenon is independent of damping and shows amplitude scaling with the ramp rate.

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Area of Science:

  • Nonlinear Dynamics
  • Mechanical Oscillations
  • Resonance Phenomena

Background:

  • The slow passage problem describes system behavior when a parameter changes slowly over time.
  • In Hopf bifurcations, oscillations are delayed past the critical parameter value.
  • Resonance in forced oscillators typically occurs near the natural frequency.

Purpose of the Study:

  • To investigate the slow passage problem through resonance in a damped, harmonically forced oscillator.
  • To compare resonance onset with the behavior observed in slow passage through Hopf bifurcations.
  • To analytically and numerically characterize the phenomenon of early resonance onset.

Main Methods:

  • Modeling a damped, harmonically forced oscillator with a linearly ramped forcing frequency.
  • Numerical simulations to observe resonance behavior.
  • Analytical treatment of the undamped oscillator for theoretical confirmation.
  • Analysis of amplitude scaling with the ramp rate (ε).

Main Results:

  • Resonance onset occurs at a 'jump frequency,' midway between the initial and natural frequencies.
  • The jump frequency is independent of the system's damping coefficient.
  • Maximal amplitude at the jump frequency scales as A~ε(-1/2), where ε is the ramp rate.

Conclusions:

  • The slow passage through resonance exhibits an 'early onset' unlike Hopf bifurcations.
  • The jump frequency provides a predictable point for resonance engagement.
  • The findings are validated through both numerical and analytical methods for damped and undamped systems.