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A method is presented which eliminates the oscillations and overshoot in a lightly damped servomechanism in a time of considerably less than one cycle of the uncompensated oscillation. The frequency response of a resonant system compensated in this manner can be made flat up through and beyond the resonant frequency of the system. For dead-beat response in one-half period, the frequency response is down only 3 db at the resonant frequency. Systems designed to have dead-beat responses in much less than one-half period have correspondingly wider bandwidths. The posicast method involves splitting up the input excitation into several fragments. Each fragment is applied at such a time that the sum of all the transient terms is equal to zero after the last excitation. The method is general and can be applied to electrical, mechanical, and even pneumatic systems.