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## Resources

Modeling Scenario

## 3-034-CarSuspension-ModelingScenario

Author(s): Therese Shelton1, Brian Winkel2

1. Southwestern University, Georgetown TX USA 2. SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: design spring-mass-dashpot spring constant underdamping car suspension suspension tolerance static equilibrium

## Abstract

We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'', meaning a single wheel.

## Citation

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## Description

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.''

## Authors

Author(s): Therese Shelton1, Brian Winkel2

1. Southwestern University, Georgetown TX USA 2. SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations