Consider the simplified quarter-car model of an automobile suspension given below where the stiffness and damping of the tire have been neglected. m b (a) Recall that the equation of motion for the given system has the form shown below. mx + bx + kx = bu + ku (b) Determine a transfer function model for the suspension where the displacement of the ground u(t) is considered the input and the displacement of the car body x(t) is con- sidered the output. (c) Consider that the car runs over a curb of height 0.05 m. In other words, the input u(t) is a step of magnitude 0.05. Let the mass of the vehicle be m = 1200 kg and the damping and stiffness of the suspension be b = 10,000 kg/s and k = 400, 000 N/m. Use the MATLAB command step to plot of the resulting motion of the car body, x(t). (d) Now build a Simulink model of the suspension according to the differential equation given above where u(t) is a unit step of magnitude 0.05. Run this simulation using the fixed step size odel (Euler) solver with time steps of 0.025, 0.01, and 0.001 seconds. Assume zero initial conditions. Plot the resulting responses x(t) on the same set of axes and explain what you see.