Dynamical response of a system of passive or active swimmers to time-periodic forcing

The presence of active forces in various biological and artificial systems may change how those systems behaves under forcing. We present a minimal model of a suspension of passive or active swimmers driven on the boundaries by time-dependent forcing. In particular, we consider a time-periodic drive from which we determine the linear response functions of the suspension. The meaning of these response functions are interpreted in terms of the storage and dissipation of energy through the particles within the system. We find that while a slowly driven active system responds in a way similar to a passive system with a re-defined diffusion constant, a rapidly driven active system exhibits a novel behavior related to a change in the motoring activity of the particles due to the external drive.