Some of us may be familiar with car suspensions, others of us clueless, and many of us in between. We can use the interplay between math/physics and cars to improve understanding of all by examining different combinations of suspension components.
A car suspension acts as a spring-mass-dashpot system on each wheel. This allows the car to stay on the road and enable good handling of the car under normal driving conditions. We examine a ``quarter car'' model that involves a second order differential equation for one wheel.
Students might refer to other sources about solutions to a second order, linear, homogeneous differential equation with constant coefficients.
A car suspension is reasonably complicated, with multiple parts and various types, and has evolved over at least five hundred years of human transportation when the passenger part of a horse-drawn carriage was ``slung from leather straps attached to four posts of a chassis that looked like an upturned table. Because the carriage body was suspended from the chassis, the system came to be known as a `suspension' - a term still used today.''