Figure 1 represents the suspension system on one of the front wheels of an automobile. The system parameters can be summarized as follows: Sprung mass M, = 300Kg My = 30Kg Ks = 60000 KT = 12000 bs = 6000N m m Unsprung mass Spring constant Tire stiffness Shock absorber constant The automobile is traveling on a level road. After 1 second of forward travel, the tire encounters a 5cm vertical obstacle (i.e.. x is a "step") that drops back down to road level after 0.1 additional seconds of forward travel. a. Using the principals of basic mechanics, draw a free body diagram of both the masses (i.e., nodes) clearly showing all the forces acting on the bodies including inertial forces. b. Find the system model (i.e. the differential equations governing the dynamic behaviour of system). Is the system model linear or non-linear? Justify your answer. c. Using MATLAB/SIMULINK, determine the position of the sprung mass, x3, and the unsprung mass, X, as a function of time. d. The primary function of the suspension system is to improve the quality of the ride by reducing the oscillations of the sprung mass. Using the model developed, investigate the effect of "tweaking" the following system parameters (change only one parameter as a time): Increasing the shock absorber constant, b,. Decreasing the spring constant, K. Increasing the unsprung mass, M, . Increasing the sprung mass, Ms. e. For each change to a system parameter answer the following questions: Does the system behave as expected? Does the quality of the ride improve? What is the physical phenomenon that is observed? f. From a practical point of view, what is a realistic lower bound on the spring constant, K, ? g. Keeping in mind the realistic lower bound on the spring constant, K, tune K, and b, to achieve the "best" ride quality. X3 X2 TWIT X Ks ms mu Forward velocity Sprung mass (vehicle body) bs -Shock absorber Unsprung mass (wheel assembly) kt Tire stiffness Elevation profile of road Figure 1: Simplified representation of automobile suspension. Figure 1 represents the suspension system on one of the front wheels of an automobile. The system parameters can be summarized as follows: Sprung mass Ms = 300 Kg M = 30 kg Unsprung mass Spring constant Ks = 60000 N/m Tire stiffness Kz = 120000 N/m Shock absorber constant bs= 6000 N's/m The automobile is traveling on a level road. After 1 second of forward travel, the tire encounters a 5 cm vertical obstacle (i.e., x is a "step") that drops back down to road level after 0.1 additional seconds of forward travel.