our model we can look at one spring of stiffness k replacing four springs (one at each wheel) of stiffness k / 4. The constant (3 describes the viscosity of the uid used in the hydraulic suspension units. We will use a sine function to model the prole of the concrete sections of the road. Thus, using the z-axis for the direction of the road, the elevation of the road is given by W) = a sin (2%) . (2) 0.1.0 D.05 D_10 Figure 2: The function h(z) for a = 0.02 m and L = 19 m Note that the period L of h(z) represents the length of the sections, while 20., the maximal change of elevation, measures how much the sections are distorted. The axes in Figure 2, where the prole of the road is given for a = 2 cm and L = 19 m, are not to scale (the amplitude is much smaller relative to the length of the sections, meaning that the actual distortions of the road are quite small). Problem 1: The car travels at constant velocity 1) in the z-direction. Find its position z(t) after time t (assuming 2(0) = 0) and insert this into (2) to nd the function y = y(t) = h(z(t)) in (1). Also nd 3'; and insert both into (1). What is the resulting differential equation