  We study the deterministic dynamics of a periodically driven particle in the
underdamped case in a spatially symmetric periodic potential. The system is
subjected to a space-dependent friction coefficient, which is similarly
periodic as the potential but with a phase difference. We observe that
frictional inhomogeneity in a symmetric periodic potential mimics most of the
qualitative features of deterministic dynamics in a homogeneous system with an
asymmetric periodic potential. We point out the need of averaging over the
initial phase of the external drive at small frictional inhomogeneity parameter
values or analogously low potential asymmetry regimes in obtaining ratchet
current. We also show that at low amplitudes of the drive, where ratchet
current is not possible in the deterministic case, noise plays a significant
role in realizing ratchet current.
