Related Experiment Video
Updated: Jun 19, 2026

Method to Measure Tone of Axial and Proximal Muscle
Published on: December 14, 2011
Resonantly driven wobbling kinks
1CSIR Computational Aerodynamics, Building 12, P.O. Box 395, Pretoria 0001, South Africa. oliver.oxtoby@gmail.com
Abstract:
The amplitude of oscillations of the freely wobbling kink in the varphi(4) theory decays due to the emission of second-harmonic radiation. We study the compensation of these radiation losses (as well as additional dissipative losses) by the resonant driving of the kink. We consider both direct and parametric driving at a range of resonance frequencies. In each case, we derive the amplitude equations which describe the evolution of the amplitude of the wobbling and the kink's velocity. These equations predict multistability and hysteretic transitions in the wobbling amplitude for each driving frequency--the conclusion verified by numerical simulations of the full partial differential equation. We show that the strongest parametric resonance occurs when the driving frequency equals the natural wobbling frequency and not double that value. For direct driving, the strongest resonance is at half the natural frequency, but there is also a weaker resonance when the driving frequency equals the natural wobbling frequency itself. We show that this resonance is accompanied by the translational motion of the kink.
Related Concept Videos
Bending and Torsional Moments
The reaction developed in a structural element when subjected to an external force causes the element to bend. When a structural element bends upwards, it creates compressive normal forces on the top and tensile normal forces on the bottom, resulting in a couple that determines the bending...
Concept of Resonance and its Characteristics
Forced Oscillations
Sound Waves: Resonance
Torsional Pendulum
As long as the rigid body's angular displacement is small, its oscillation can be modeled as a linear angular oscillation. The amplitude of the oscillation is an angle. The role of mass is played by the...
Damped Oscillations
Although friction and other non-conservative...

