Figure shows a vehicle model on a horizontal plane. The car has a mass 1000 kg with mass moment of inertia Jo = 2000 kg.m about its center of gravity (COG). The total stiffness at the front wheels is equal to k, and the total stiffness at the rear wheels is k. The vehicle can be assumed of having two degrees of freedom, vertically in the direction of x and rotationally in direction about its COG. a. If k = 1500 N/m, k = 1500 N/m and L = 2 m, L = 2.5 m, determine the natural frequencies and mode shapes of the automobile. Normalize the mode shapes to the first row. b. Figure out how to uncouple the system and after that derive the equation of motion for uncouple system. For this new uncouple system, set the suitable spring stiffness for k, if k, is maintained at 1500 N/m. x(t) COG nd Ll 12