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3-060-DataToDifferentialEquation-ModelingScenario

Author(s): Eric Sullivan1, Kelly Cline1

Carroll College, Helena MT USA

Keywords: Association & Data Fitting mass spring-mass system spring\ total distance numerical differentiation

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Abstract

Resource Image Students use knowledge of second-order linear differential equations in conjunction with physical intuition of spring-mass systems to estimate the damping coefficient and spring constant from data.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Vision and Change Core Competencies - Ability
Principles of How People Learn

Description

The data is presented as total distance traveled instead of displacement so the students must rely on previous calculus knowledge as well as knowledge of differential equations and numerical differentiation.

A motion sensor was set up to measure the motion in a spring-mass system, but something went wrong and the motion sensor measured the total distance traveled instead of simply measuring the distance from the sensor. The experiment was conducted three times (same spring and same mass) with different initial conditions. The total distance traveled is given as the data sets in the Excel spreadsheet

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Authors

Author(s): Eric Sullivan1, Kelly Cline1

Carroll College, Helena MT USA

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