Related Experiment Video
Updated: Mar 15, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
9.8K
Tilted excitation implies odd periodic resonances
G I Depetri1,2, J C Sartorelli2, B Marin2,3
1Instituto de Física "Gleb Wataghin," Universidade Estadual de Campinas, 13083-859 Campinas, SP, Brazil.
Physical Review. E
|August 31, 2016
Summary
Breaking symmetry in parametric systems, like a tilted pendulum, creates new odd resonances. This phenomenon, explained by the Melnikov method, arises from an additional torque in asymmetric systems.
Area of Science:
- Nonlinear Dynamics
- Mechanical Vibrations
- Symmetry Breaking
Background:
- Parametric systems exhibit complex resonance behaviors.
- Symmetry plays a crucial role in determining system dynamics.
- Understanding resonance shifts is key in mechanical and physical systems.
Purpose of the Study:
- To investigate the impact of broken symmetry on parametric system resonances.
- To elucidate the emergence of odd resonances in asymmetric systems.
- To provide analytical and numerical explanations for observed phenomena.
Main Methods:
- Numerical simulations of parametric systems.
- Experimental validation using a physical pendulum model.
- Analytical determination using the Melnikov subharmonic function.
Main Results:
- Odd resonances were observed and confirmed experimentally and numerically.
- The Melnikov method successfully predicted saddle-node bifurcations.
- An extra torque in asymmetric cases was identified as the cause of odd resonances.
Conclusions:
- Broken symmetry in parametric systems leads to the appearance of odd resonances.
- The Melnikov method provides a robust framework for analyzing these asymmetric effects.
- The findings offer insights into controlling and predicting resonance behavior in complex systems.
Related Concept Videos
01:19Concept of Resonance and its Characteristics
6.8K
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...
6.8K
01:04Oscillations about an Equilibrium Position
7.1K
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
7.1K
01:23Parallel Resonance
708
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:
708
01:06Forced Oscillations
8.2K
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.
8.2K
01:14Sound Waves: Resonance
3.6K
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...
3.6K
01:21Properties of Fourier series II
697
Time scaling of signals is a crucial concept in signal processing that affects the Fourier series representation without altering its coefficients. The process modifies the fundamental frequency, thereby changing how the series represents the signal over time. This principle is essential in various applications, including audio and image processing, where signal manipulation is frequent. Understanding function symmetries is fundamental to simplifying the Fourier series.
A function f(t) is...
A function f(t) is...
697