A shock absorber with nth order stiffness and mth order damping is designed for optimum response to a step change in base velocity (an acceleration impulse). The objective of the design is to minimize the maximum acceleration level occurring during the transient response. A single constraint is used to limit relative motion between the base and the isolated mass and another constraint is added to limit the oscillatory nature of the system response. Results of the study are presented on dimensionless curves showing the optimum stiffness and damping coefficients and the expected system performance as functions of m and n. Optimization methods used in the problem involve nonlinear programming and numerical solution of the governing differential equations. Effectiveness of the approximate parameter optimization scheme suggested by Sevin and Pilkey is also considered.

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