To have mass m and its suspension system is modeled as a linear viscous damper with damping constant b in parallel to a linear spring with stiffness k and length at rest l0. the vertical position of the car is denoted by zm(t), it is being driven at constant horizontal speed u, and the wheel at point w always remains in contact with the road with profile given as r(x), see, fig. 2. 1) a) show that for a given road profile r(x), the vertical position of the wheel at point w can be written as a function of time zw (t) = r(u t). b) using newton’s second law and accounting for gravity and the weight of the car, write down the ode satisfied by the vertical position zm(t) of the car and compute the vertical position z (0) m of the car when it is stopped (u = 0 m/s), at rest, on a flat road (r(x) = 0 m).