  We treat the noise-activated escape from a one-dimensional potential well of
an overdamped particle, to which a periodic force of fixed frequency is
applied. We determine the boundary layer behavior, and the physically relevant
length scales, near the oscillating well top. We show how stochastic behavior
near the well top generalizes the behavior first determined by Kramers, in the
case without forcing. Both the case when the forcing dies away in the weak
noise limit, and the case when it does not, are examined. We also discuss the
relevance of various scaling regimes to recent optical trap experiments.
