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. (C) 2014 Elsevier B.V. All rights reserved.