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## Resources Modeling Scenario

## 3-002-ModelsMotivatingSecondOrder-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: resistance spring mass oscillation Hooke's Law dampening

## Abstract Ordinary differential equations involve second derivatives and second derivatives appear in many contexts, chief among them are the study of forces and resulting motion. This is principally because of Newton's Second Law of Motion.

## Citation

Researchers should cite this work as follows:

## Description

We will be modeling a spring mass system and seeing how well it describes data taken from an experiment.

Consider the abstract diagram for the mass at the end of the spring.

We will presume that the mass is settled into a static equilibrium in which the force due to gravity is countered by the restoring force of the spring to contract or expend depending upon whether the mass is below or above this static equilibrium point, respectively, and hence, pull up or push down, respectively, the mass.

Suppose we let y(t) be the distance the mass is from static equilibrium and y(t)>0 for when the mass is below the static equilibrium, i.e. when the spring is extended, and y(t)<0 for when the mass is above the static equilibrium, i.e. when the spring is compressed.

## Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations