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Shock Response (Half-Sine)

A shock pulse hits different structures differently. What matters is the ratio of the pulse duration to the item's natural period. Soft mounts (low f_n) filter the pulse; stiff ones just follow it; in between it amplifies — up to about 1.77× for an undamped half-sine.

Pulse amplitude (G)

Pulse duration (ms)

Natural frequency fn (Hz)

Damping ratio ζ

Peak response

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Amplification

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fn × duration

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Computed by direct integration of a single-degree-of-freedom system. Classic MIL-STD-810 pulses: 11 ms / 20 G, 6 ms / 40 G.

A helper, not a substitute for engineering judgment. Verify against the governing standard.