Where does resonance collide?

The large response of an oscillating system when it is driven at a frequency close to its own natural frequency, so that each push arrives in step with the motion and the amplitude builds until damping balances the drive. French's textbook treatment gives the response curve, its peak at the natural frequency and its width set by the damping. The standard classroom example is wrong: Billah and Scanlan showed in 1991 that the Tacoma Narrows bridge of 1940 was destroyed by aeroelastic flutter, a self-excited instability, not by wind gusts matching a natural frequency, and that the textbooks had repeated the error for fifty years. Resonance here is a relation between a driving frequency and a system's own, and it has a number.[1][2]

Unit

A driven oscillating system, at a driving frequency

Recovery means

Not applicable, the criterion is the ring-down: how fast the amplitude decays when the drive stops

Measured by

Amplitude or power against driving frequency; the resonant frequency and the quality factor Q

The absorption and re-emission of radio-frequency energy by atomic nuclei in a magnetic field, at a frequency set by the field strength, and the imaging built on it. The physics is the resonance of the previous spoke applied to precessing nuclei. Lauterbur showed in 1973 that a gradient in the field makes the resonant frequency depend on position, so that the signal can be turned into an image; Mansfield and Grannell published the same idea the same year in terms of diffraction. Clinical practice dropped the word nuclear and kept resonance. A radiologist reading an MRI is using the physics meaning exactly, and none of the social meanings at all.[3][4]

Unit

Hydrogen nuclei in a voxel of tissue, in a scanner

Recovery means

Relaxation, the return of nuclear magnetisation to equilibrium, whose time constants T1 and T2 give the image its contrast

Measured by

Signal intensity by voxel; relaxation times; the Larmor frequency at a given field strength

The top of Keller's customer-based brand equity pyramid: the state in which customers feel in sync with the brand, expressed as loyalty, attachment, a sense of community with other users, and active engagement beyond purchase. Keller fixed the model in a 2001 Marketing Science Institute report that builds from salience through performance, imagery, judgements and feelings to resonance, and his 2003 synthesis placed it inside a multidimensional account of brand knowledge. Resonance here is a property of a customer's relationship with a brand, achieved at the end of a sequence, and the measure is what the customer does and says. No frequency is involved, and the word means intensity and fit.[5][6]

Unit

A customer's relationship with one brand

Recovery means

Not applicable, the criterion is depth: whether the relationship reaches loyalty, attachment, community and engagement

Measured by

Repeat purchase and share of category; self-reported attachment, community identification, and engagement behaviours

The degree to which a movement's interpretive frame strikes a chord with the people it hopes to mobilise, so that they take it up. Snow, Rochford, Worden and Benford introduced frame alignment in 1986, and Snow and Benford named resonance in 1988 as the variable that decides which frames mobilise: a frame that is empirically credible, fits the audience's experience and matches their cultural narratives resonates, and one that does not fails whatever its logic. Benford and Snow's 2000 review sorted the conditions into credibility (consistency, empirical fit, credible articulators) and salience, centrality, experiential commensurability, narrative fidelity. Resonance here is a fit between a message and a culture, judged by whether people act on it.[7][8][9]

Unit

A frame, in relation to a target audience, during a mobilisation

Recovery means

Not applicable, the criterion is mobilisation: whether the frame recruits and sustains participants

Measured by

Participation and recruitment following frame deployment; content analysis of frames against audience beliefs

A mode of relating to the world in which something touches us, we respond, both sides are changed, and the outcome cannot be forced. Rosa fixed the concept in 2016, in English in 2019, as the answer to alienation: a life is good not when it has more of the world within reach but when it stands in resonant relations along horizontal axes to other people, diagonal axes to things and work, and vertical axes to nature, art, history and religion. The four marks are being affected, responding with self-efficacy, being transformed, and the unavailability of the result to control. Susen's 2020 review took the theory's measure and pressed on whether a relation nobody can command can ground a critique of society. Resonance here is normative (a criterion for a good life) and is defined by its opposite.[10][11]

Unit

A person's relation to a domain of the world, over a life

Recovery means

Not applicable, the criterion is the relation itself, and Rosa holds that it cannot be produced on demand

Measured by

Not measured; reconstructed from experience, interviews and cultural diagnosis

The description of a molecule's electronic structure as a combination of two or more valence-bond structures, none of which is the molecule on its own, with the actual state lower in energy than any of them. Pauling fixed the idea in 1931 and gave it the field's textbook in 1939: benzene is not alternating between two Kekulé structures but is a single hybrid of them, and the extra stability is the resonance energy. The name came from Heisenberg's quantum-mechanical treatment of exchange, which had borrowed it from coupled oscillators, and Pauling insisted that nothing oscillates: the structures are a bookkeeping device and the resonance is between drawings. This is the one meaning on the page in which resonance is explicitly not a motion.[12][13]

Unit

A molecule, in its ground electronic state

Recovery means

Not applicable, the criterion is stabilisation: the energy gap between the hybrid and its best single structure

Measured by

Resonance energy from heats of hydrogenation or formation; bond lengths intermediate between single and double