This article presents the results of a study on computer-aided design and dynamic analysis of a simplified mechanical system, as well as the synthesis of passive mechanical control for a rear suspension system. This system was introduced in the new ground effect cars following the 2022 Formula 1 technical regulation changes. The first part of the manuscript outlines the problem of interest, detailing the methodological approach and mathematical framework used in the research. The second part focuses on the numerical experiments conducted to design components that meet the suspension system requirements. The study demonstrates that an active suspension can be designed using components that passively vary stiffness and damping parameters through specific mechanisms. A simplified mechanical system model was also developed, and dynamic simulations of its nonlinear behavior were performed using MATLAB. These simulations allowed for the extrapolation of the elastic and damping characteristics. Finally, a functional CAD model of the proposed solution was created in SOLIDWORKS, particularly ensuring proper component functionality within the limited available space.