  To address the dynamics of a Brownian particle on a periodic symmetric
substrate under high-frequency periodic forcing with a vanishing time average,
we construct an effective Langevin dynamics by invoking Kapitza-Landau time
window. Our result is then exploited to simulate the mobility both for original
and effective dynamics which are in good agreement with theoretical
predictions. This close agreement and the enhancement of mobility are very
robust against the tailoring of amplitude-to-frequency ratio which
substantiates the correctness of our calculation. Present results may be
illuminating for understanding the dynamics of cold atoms in electromagnetic
fields.
