  We study the zero temperature non-equilibrium dynamics of a fermionic
superfluid in the BCS limit and in the presence of a drive leading to a time
dependent chemical potential $\mu(t)$. We choose a periodic driving protocol
characterized by a frequency $\omega$ and compute the fermion density, the
wavefunction overlap, and the residual energy of the system at the end of $N$
periods of the drive. We demonstrate that the BCS self-consistency condition is
crucial in shaping the long-time behaviour of the fermions subjected to the
drive and provide an analytical understanding of the behaviour of the fermion
density $n_{{\mathbf k}_F}$ (where ${\mathbf k}_F$ is the Fermi momentum
vector) after a drive period and for large $\omega$. We also show that the
momentum distribution of the excitations generated due to such a drive bears
the signature of the pairing symmetry and can be used, for example, to
distinguish between s- and d-wave superfluids. We propose experiments to test
our theory.
