  We study the dynamics of a glassy model with infinite range interactions
externally driven by an oscillatory force. We find a well-defined transition in
the (Temperature-Amplitude-Frequency) phase diagram between (i) a `glassy'
state characterized by the slow relaxation of one-time quantities, aging in
two-time quantities and a modification of the equilibrium
fluctuation-dissipation relation; and (ii) a `liquid' state with a finite
relaxation time. In the glassy phase, the degrees of freedom governing the slow
relaxation are thermalized to an effective temperature. Using Monte-Carlo
simulations, we investigate the effect of trapping regions in phase space on
the driven dynamics. We find that it alternates between periods of rapid motion
and periods of trapping. These results confirm the strong analogies between the
slow granular rheology and the dynamics of glasses. They also provide a
theoretical underpinning to earlier attempts to present a thermodynamic
description of moderately driven granular materials.
