  We introduce two tractable analytical models to describe dynamic effects at
resonant light scattering by subwavelength particles. One of them is based on
generalization of the temporal coupled-mode theory, and the other employs the
normal mode approach. We show that sharp variations in the envelope of the
incident pulse may initiate unusual, counterintuitive dynamics of the
scattering associated with interference of modes with fast and slow relaxation.
To exhibit the power of the models, we apply them to explain the dynamic light
scattering of a square-envelope pulse by an infinite circular cylinder made of
$GaP$, when the pulse carrier frequency lies in the vicinity of the destructive
interference at the Fano resonances. We observe and explain intensive sharp
spikes in scattering cross section just behind the leading and trailing edges
of the incident pulse. The latter occurs when the incident pulse is over and is
explained by the electromagnetic energy released in the particle at the
previous scattering stages. The accuracy of the models is checked against their
comparison with results of the direct numerical integration of the complete set
of Maxwell's equations and occurs very high. The models' advantages and
disadvantages are revealed, and the ways to apply them to other types of
dynamic resonant scattering are discussed.
