Definition 0.1   The very sharp (or marked) increase in amplitude of oscillation of a mechanical, electrical or nuclear system exposed to a periodic force , or another oscillator whose frequency is equal to, or very close to, the natural undamped frequency of the oscillating system . The intensity of oscillation is defined as the square of the amplitude of the oscillations. More precisely, in the case of a linear oscillator with a resonance frequency , the intensity of oscillations when the system is driven with a driving frequency is given by:

This oscillator intensity is a Lorentzian function which is characteristic of many resonant systems, with being known as the linewidth of the resonance, or resonance linewidth at half-heigth of the resonance peak which depends on the degree of damping of the oscillator.

Remark 0.1   Heavily damped oscillators have broad linewidths, and will respond to a wider range of driving frequencies near the resonance frequency. The resonance linewidth is inversely proportional to the quality factor, or -factor of the oscillating systems, which is a measure of the sharpness of their resonance. As an example, for NMR and rf electrical circuit probes, a high Q-factor is essential for high sensitivity detection of the signal by the rf probe.

Definition 0.2   A system is called resonant if it has the property of oscillating by itself (without external coupling) with a maximum amplitude only at a certain frequency or frequencies, known as the resonance frequencies of the system.