We discuss two mechanical systems in which the approximate equations of motion are the same as the rapid adiabatic passage of a two-state quantum-mechanical system, such as that which occurs with quasistatic interactions and from the quasiperiodic action of a chirped-frequency laser pulse. We discuss a pair of masses on springs, weakly coupled by another spring, one of whose spring constants varies slowly, and a pair of coupled pendula, where the length of one pendulum slowly changes. In each example an approximation analogous to the rotating-wave approximation used in the corresponding quantum system brings the second-order macroscopic equations of motion into first-order form, and a slow variation in a system parameter characteristic leads to adiabatic change and rapid adiabatic passage.
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