This paper is concerned with the development of a new approach for integrated design of controlled mechanical systems. The contribution is three fold. We first show through a typical design example that the closed-loop bandwidth achievable with a reasonable control effort is shown to be closely related to the frequency range for which the plant is high gain and exhibits positive-realness when high gain controllers are not allowed. Secondly, we present matrix inequality characterizations of the robust finite frequency positive-real property and the finite frequency high gain property. Thirdly, we propose a systematic method for designing mechanical systems to achieve the finite frequency properties. Then, the the method is applied to the shape design of a swing-arm for magnetic storage devices and the smart structure design using piezo-electric films in order to confirm the validity of the proposed method.