  The analytic description of ac-driven elastic interfaces in random potentials
is desirable because the problem is experimentally relevant. This work
emphasises on the mean field approximation for the problem at zero temperature.
We prove that perturbation theory is regular in all orders by giving an
inductive scheme how to find groups of ill-behaved graphs that mutually cancel,
leaving a regular expression. In the parameter regimes for which perturbation
theory is applicable it agrees with numerical results. Further, we determine
the dependence of the Fourier coefficients of the mean velocity on the
parameters of the model.
