  We present a classical analysis of the transient response of Josephson
junctions perturbed by microwaves and thermal fluctuations. The results include
a specific low frequency modulation in phase and amplitude behavior of a
junction in its zero-voltage state. This transient modulation frequency is
linked directly to an observed variation in the probability for the system to
switch to its non-zero voltage state. Complementing previous work on linking
classical analysis to the experimental observations of Rabi-oscillations, this
expanded perturbation method also provides closed form analytical results for
attenuation of the modulations and the Rabi-type oscillation frequency. Results
of perturbation analysis are compared directly (and quantitatively) to
numerical simulations of the classical model as well as published experimental
data, suggesting that transients to phase-locking are closely related to the
observed oscillations.
