Min-Max Solutions for the Linear Mass-Spring System

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Abstract
Absolute upper and lower bounds have been determined for the maximum displacement of an undamped linear mass-spring system acted on by a non-negative forcing function characterized only by total impulse and duration. The upper bound is shown to result from applying the total impulse to the mass as an initial blow. The lower bound is shown to depend upon the ratio of load duration to natural period of the system, and this response results from a forcing function consisting of an initial and final impulse and an intermediate constant force. In the latter case, for sufficiently short durations, the forcing function reduces simply to equal initial and final impulses.

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