When a vehicle performs planar motion, the tire side force induces a jacking-up effect determined by the suspension roll center height governed by suspension geometry. These jacking forces also excite pitching motion. In this study, the pitching degree of freedom, along with roll degree of freedom, was incorporated in the bicycle model of the vehicle motion, hence it becomes four-degree-of-freedom model, and a new analytical method that applies modal analysis method to the model decomposes the motion of the sprung mass of the vehicle into mutually independent vibration modes. Since the superposition of these vibration modes can reproduce vehicle motion, these vibration modes are the fundamental factors governing sprung-mass behavior. Therefore, understanding how these vibration modes respond to design parameters provides a theoretical foundation to design desired vehicle dynamics from the early stage of car development. This report presents, by conducting modal analysis of the four-degree-of-freedom model, that the pitching dominant mode and the mode associated with planar motion and roll, which constitute a three-degree-of-freedom system, are mutually independent dynamically. Furthermore, the suspension design method that controls the pitch-dominant mode can ameliorate the initial turn-in response of the sprung mass in the desirable direction. The insight presented in this report can offer a systematic understanding of the essential characteristics of sprung mass dynamics and can provide new theoretical framework for vehicle dynamics performance design.