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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

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Abstract

Resource Image 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.

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Article Context

Resource Type
Differential Equation Type
Qualitative Analysis
Application Area
Lesson Length
Technology
Approach
Skills
Pedagogical Approaches
Bloom's Cognitive Level

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.''

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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

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