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However, resonance can also be detrimental, leading to excessive vibrations or even structural failure in some cases. [3] All systems, including molecular systems and particles, tend to vibrate at a natural frequency depending upon their structure; this frequency is known as a resonant frequency or resonance frequency.
Thus, the lifetime of a particle is the direct inverse of the particle's resonance width. For example, the charged pion has the second-longest lifetime of any meson, at 2.6033 × 10 −8 s. [2] Therefore, its resonance width is very small, about 2.528 × 10 −8 eV or about 6.11 MHz. Pions are generally not considered as "resonances".
Contributing structures of the carbonate ion. In chemistry, resonance, also called mesomerism, is a way of describing bonding in certain molecules or polyatomic ions by the combination of several contributing structures (or forms, [1] also variously known as resonance structures or canonical structures) into a resonance hybrid (or hybrid structure) in valence bond theory.
Clar's rule states that for a benzenoid polycyclic aromatic hydrocarbon (i.e. with only hexagonal rings), the resonance structure with the largest number of disjoint aromatic π-sextets is the most important to characterize its chemical and physical properties. Such resonance structure is called the Clar structure. In other words, a polycyclic ...
The resonance condition is given by = , which is when the neutrino system experiences resonance and the mixing becomes maximal. For very small θ , {\displaystyle \ \theta \ ,} this condition becomes ℓ ν ≈ ℓ 0 , {\displaystyle \ \ell _{\nu }\approx \ell _{0}\ ,} that is, the eigenfrequency for a system of mixed neutrinos becomes ...
Poincare observed that in many cases, there are integer linear combinations of the eigenvalues that sum to zero; this is the original resonant interaction. When in resonance, energy transfer between modes can keep the system in a stable phase-locked state. However, going to second order is challenging in several ways.
A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator can be either electromagnetic or mechanical (including acoustic). Resonators are used to either ...
The rotating-wave approximation is an approximation used in atom optics and magnetic resonance. In this approximation, terms in a Hamiltonian that oscillate rapidly are neglected. This is a valid approximation when the applied electromagnetic radiation is near resonance with an atomic transition, and the intensity is low. [1]