A computer methodology is presented that relates the dynamic response of a geometrically constrained, articulated mechanical system to changes in the design variables. The purpose of the methodology is to obtain the optimum design under dynamic conditions. The methodology finds the eigensolution to the linearized system equations of motion and then computes the rates of change of the eigenvalues and eigenvectors with respect to the system design variables. The design is modified to improve the system dynamic characteristics based on the sensitivity of the design variables changes. This methodology is demonstrated by evaluating the sensitivity of the natural frequencies and modes of vibration for an agricultural tractor-trailer system with changes to vehicle parameters for reduced ride vibration levels.