  If the duration of the input pulse resonantly interacting with a system is
comparable or smaller than the time required for the system to achieve the
steady state, transient effects become important. For complex systems, a
quantitative description of these effects may be a very difficult problem. We
suggest a simple tractable model to describe these phenomena. The model is
based on approximation of the actual Fourier spectrum of the system by that
composed of the superposition of the spectra of uncoupled harmonic oscillators
(normal modes). The physical nature of the underlying system is employed to
select the proper approximation. This reduces the dynamics of the system to
tractable dynamics of just a few driven oscillators. The method is simple and
may be applied to many types of resonances. As an illustration, the approach is
employed to describe the sharp intensive spikes observed in the recent
numerical simulation of short light pulses scattered by a cylinder in the
proximity of destructive Fano interference [Phys. Rev. A., vol. 100, 053824
(2019)] and exhibits excellent agreement with the numerics.
