<div class="htmlview paragraph">A competing variables approach is developed for determining an optimal choice of stiffness and damping for minimization of the dynamic response of a single-degree-of-freedom (SDOF) system subjected to random base excitation. Two constrained optimization problems are solved, one formulated as a minimization of the mean square absolute acceleration of the mass &lt;ÿ²&gt; subject to the inequality constraint &lt;x²&gt;≤ x²_o, where &lt;x²&gt; represents the mean square relative displacement between the mass and its support, and &lt;x²&gt; is a prescribed constant. The other solved problem is formulated as minimization of &lt;x²&gt; subject to &lt;ÿ²&gt; ≤ a²_o, where is a prescribed constant. An application is made to the problem of selecting optimal parameters for an oscillator subjected to the 1940 El Centro earthquake ground acceleration, and comparisons between the predictions of the simple theory and the results of extensive numerical simulations are presented.</div>