Figure 1 shows the wheel suspension system for a car. The wheel follows the road given by the position x, (t). x(t) x (1) B M1 M2 ODD K1 K2 x (1) Figure 1 Wheel suspension system a) Apply Newton's laws to each of the two masses to derive the equations for the vertical motion of the wheel and the car, using the symbols in the Figure 1. b) Use the values M, = 40 kg, M, = 250 kg, B = 500 Ns/m, K, = 20000 N/m and K = 10000 N/m, and write the equations on numerical form, separating x, and x- c) Derive the transfer function from the road position x, (t) to the car motion x (t), h(s) = 2(1) Xo(t) d) You can now tune the different parameters to obtain your perfect driving experience. Write a simulation diagram for the model. Analyse the model in Simulink. e) Introduce the states , = x, = x, x, 2x, and u = xo. Write the equations derived above as four first order differential equations. With x (t) as input to the system and wheel position x, and car position x as measurements, introduce the state space model.