The shock response of nonlinear single-degree-of-freedom systems is analytically obtained by straight-line-segments approximation. The initial conditions of the
n' th phase are equal to the boundary conditions of the (
n-1)'th phase at the refracting point, and the n'th phase solution is similarly obtained to the (
n-1)' th one's. It is better to determine the suitable line-segments by Ergin's method (E. I. Ergin: J. Appl. Mech. 23 (1956) 635), but is not necessary for the rough approximation. The calculated values of displacement and its time duration to the maximum response for polyurethane foam are rather greater (about 10%) than the experimental values. Damping gives a severe influence upon appearing spring constant at high speed testing.
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