This paper discusses a vibration control algorithm for a single degree of freedom model under non-stationary random disturbances. Selecting an appropriate set of passive mechanical parameters under a given feedback gain minimizes the energy requirement for the controller. This optimum selection is probabilistically obtained under stationary random process. It is also proved that the same optimum parameter selection minimizes the force requirement for the controller. The stochastically expected optimum parameter set is numerically evaluated in the time domain under non-stationary random excitations. The deterministic analyses ascertained that the control energy converges to zero as the time goes to infinity under any non-stationary random disturbances.