  We study the excitation dynamics of Fano resonance within the classical model
framework of two linear coupled oscillators. An exact solution for the model
with a damped harmonic force is obtained. The details of growth a Fano profile
under the harmonic excitation is shown. For incident ultra-wideband pulse, the
reaction of a system becomes universal and coincides with the time-dependent
response function. The results of numerical calculations clarify two
alternative ways for experimental measurement of the complete characteristics
of a system: direct observation of the system response to a monochromatic force
by frequency scanning or recording of time-dependent response to the
delta-pulse. As a specific example, time-dependent excitation in a system
consisting of a quantum dot and a metal nanoparticle is calculated. Then it is
shown the applicability of the extended model of damped oscillators with
radiative correction to describe the build-up a plasmon Fano resonance in a
scattering of a femtosecond laser pulse by nanoantenna.
