  The spectral response and physical features of the 2D Hubbard-Holstein model
are calculated both in equilibrium at zero and low chemical dopings, and after
an ultra short powerful light pulse, in undoped systems. At equilibrium and at
strong charge-lattice couplings, the optical conductivity reveals a 3-peak
structure in agreement with experimental observations. After an ultra short
pulse and at nonzero electron-phonon interaction, phonon and spin subsystems
oscillate with the phonon period $T_{ph} \approx 80$ fs. The decay time of the
phonon oscillations is about 150-200 fs, similar to the relaxation time of the
charge system. We propose a criterion for observing these oscillations in high
$T_c$ compounds: the time span of the pump light pulse $\tau_{pump}$ has to be
shorter than the phonon oscillation period $T_{ph}$.
