Antiresonance Antiresonance In the physics of coupled oscillators, antiresonance, by analogy with resonance, is a pronounced minimum in the amplitude of one oscillator at a particular frequency, accompanied by a large shift in its oscillation phase. Such frequencies are known as the system's antiresonant frequencies, and at these frequencies the oscillation amplitude can drop to almost zero. Antiresonances are caused by destructive interference, for example between an external driving force and interaction with another oscillator. Antiresonances can occur in all types of coupled oscillator systems, including mechanical, acoustic, electromagnetic and quantum systems. They have important applications in the characterization of complex
Tune shift with amplitude by a Hamiltonian, or a symplectic map. For each initial position, we follow the particle as it traces out its orbit. After transformation into action-angle coordinates, one compute the tune formula_1 and the action formula_2. The tune shift with amplitude is then given by formula_3. The transformation to action-angle variables out of which the tune may be derived may be considered as a transformation to normal form. The tune shift with amplitude is important as a measure of non-linearity of a system. A linear system will have no tune shift with amplitude. Further, it can be important regarding the stability