One way to model a vehicle is as a massive object that is connected by springs and shock absorbers to the wheels. Here is a simple model:

Question

There is a mass m suspended by a spring with spring constant k and a oil-filled shock-absorber with viscous friction constant b over a wheel base. The wheels ride over a rough road that moves up and down. We will only model the vertical motion, with vertical displacement y. If you remember your basic physics you will be able to see that the balance-of-forces equation governing the motion in the y direction is just a second-order linear constant-coefficient ordinary differential equation:

md2y(t)dt2+bdy(t)dt+k(y(t)−Yroad(t))=0