It is a challenge to design vehicle for good ride characteristics to the engineer, given the many design constraints. The vibration environment is a very important criterion by which people judge the design and construction “ride quality” of a car. It needs a quarter - vehicle mathematical model to describe the dynamic motions of a vehicle on the road.
In this paper, LaGrange Equation is used to derive the equations of motion. A state - space formulation is obtained by using state variables. And the characteristic equation, natural frequency and damping ratio are achieved. Through the analytical and numerical study on the ride quality of a quarter - vehicle (2 - DOF, 0 - dimension) model, the dynamic behavior of vehicle is represented by simulating the input, which is single-input-single-output (SISO) - output relationship. * The effects of mass ratio, stiffness ratio and damping coefficient ratio on the vibration of the sprung mass are researched.