Problem 4. Figure 4 shows a schematic diagram of an automobile suspension system. As the car moves along the road, the vertical displacements at the tires act as the motion excitation

to the automobile suspension system. The motion of this system consists of a translational motion of the center of mass and a rotational motion about the center of mass. Mathematical modeling of the complete system is quite complicated. A very simplified version of the suspension system is shown in Figure 3-b. Assuming that the motion x; at point P is the input to the system and the vertical motion x, of the body is the output, obtain the transfer function (Consider the motion of the body only in the vertical direction.) Displacement x, is measured from the equilibrium position in the absence of input x₁. Center of mass Auto body (a) Figure 4 www P (b) 3₂