You are analyzing a conventional suspension system for a passenger car considering the model shown in Figure 1. Assume the total sprung mass of the vehicle is 1400 kg, and the total unsprung mass is 150 kg. Also, assume that the suspension stiffness is 66.793 kN/m, the tire stiffness is 201 kN/m, and suspension damping coefficient is 1189 N s/m. Also, assume the all the suspension system components have identical values on all axles. Perform the following tasks: . sprung mass suspension unsprung mass tire kt mb mw www. Xb MT Xw Figure 1: Suspension system quarter vehicle model 1. Derive the transfer function in symbols. 2. Using MATLAB, find the output (X) for the following inputs (X): (a) Step in the road from 0 to 3 cm after 20 meters from the starting point. See Figure 2(a). Xr (m) 20 (a) 100 X (m)