Abstract: The motion of a mechanical stage may be directed in x-, y-, and/or z-dimensions such that excitation of a resonant frequency f is reduced. In particular, once a resonant frequency f is identified, the acceleration of the stage in the x-, y-, and/or z-dimensions may divided into an even number of acceleration segments or intervals, with the second of each pair of acceleration segments starting 1/(2f) seconds after the start of the initial acceleration segment. The acceleration intervals may be defined by a start time, an amplitude profile, and/or a time duration. In some implementations, the amplitude and time duration of each acceleration pulse may be different. The amplitude and time duration of acceleration steps may be determined and adjusted to compensate for the particular resonance frequency of an individual system, and programmed into a controller for the stage using motor programming controls.