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We present a classical analysis of the Josephson response to externally applied microwave fields. We are specifically interested in the dynamical response of the system to microwave perturbations, since this has recently been intensely investigated experimentally due to signatures of macroscopic quantum behavior. The analysis of the standard classical model of Josephson systems (pendulum models) shows that many features, similar to what the experiments are reporting, can be observed in the purely classical Josephson system.

The classical features of interest arise from the dynamical response and transients to phase-locking of the oscillator to the external microwave signal. We exemplify the classical picture by making comparisons between the classical analysis and a few experimental observations of multi-peak switching distributions, Rabi-type oscillations, Ramsey-type fringes, and spin-echo type response as derived from the microwave-induced escape from the potential well of a Josephson system.