
3091SMassSpringExperiments
14 Jan 2022   Contributor(s):: Bonnie Moon
In this lab students will collect data on their spring mass systems and compare their empirical models to their theoretical ones—giving them an opportunity to actually test a model against data. Before this lab, students should have modeled springmass systems and solved secondorder...

3073SEarthQuake Part II
06 Aug 2021   Contributor(s):: Tracy Weyand
This modeling scenario considers a onestory building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a massspringdamper system. In this activity, students will analyze motion of the roof under different damping and vibration...

3072SEarthQuake Part I
06 Aug 2021   Contributor(s):: Tracy Weyand
This modeling scenario considers a onestory building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a massspring system. In this activity, students will analyze the motion of the roof caused by ground movement. Here we...

1128SRocketFlight
04 Jun 2020   Contributor(s):: Brian Winkel
We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its fall to earth.

3026SSpringInverseProblem
29 May 2020   Contributor(s):: Brian Winkel
We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.

2018Yu, Polly Y. and Gheorghe Craciun  Mathematical Analysis of Chemical Reaction Systems.
05 Apr 2020   Contributor(s):: Brian Winkel
Yu, Polly Y. and Gheorghe Craciun. 2018. Mathematical Analysis of Chemical Reaction Systems. Isr. J. Chem. 58: 1 – 10.See https://people.math.wisc.edu/~craciun/PAPERS_NEW/Yu_Craciun_2018Israel_Journal_of_Chemistry.pdf .Abstract: The use of mathematical methods for the...

2009Chellaboina, Vijaysekhar, Sanjay P. Bhat, Wassil M. Haddad, Dennis S. Bernstein  Modeling And Analysis  Mass Action Kinetics.
26 Mar 2020   Contributor(s):: Brian Winkel
Chellaboina, Vijaysekhar, Sanjay P. Bhat, Wassil M. Haddad, Dennis S. Bernstein. 2009. Modeling And Analysis  Mass Action Kinetics. IEEE Control Systems Magazine. August. 6078.See https://ieeexplore.ieee.org/document/5184956. From the Introduction:"Massaction...

2017Goulet, D.  Modeling, Simulating, and Parameter Fitting of Biochemical Kinetic Experiments.
20 Mar 2020   Contributor(s):: Brian Winkel
Goulet, D. 2017. Modeling, Simulating, and Parameter Fitting of Biochemical Kinetic Experiments. SIAM REVIEW. 58(2): 331–353.See https://locus.siam.org/doi/abs/10.1137/151004707 .Abstract. In many chemical and biological applications, systems of differential equations containing...

1083SFallingMeteorites
24 Aug 2019   Contributor(s):: Lyle Clifford Smith
After introducing the solution to the ordinary differential equation which models a falling object with drag (firstorder, nonlinear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...

1107SClothDry
27 Apr 2019   Contributor(s):: Brian Winkel
We build a mathematical model for the rate at which drying takes place in a cloth wet with water while hanging in air. A model can be based on underlying physical principles. Such a model is called an analytic model. Or your model could be based on observations and reasoned terms in your...

2017Stan, GuyBart  Modelling in Biology.
02 Sep 2017   Contributor(s):: Brian Winkel
2017. Stan, GuyBart. Modelling in Biology. Class Notes. Imperial College of London. 71 pp.Keywords: differential equation, model, stability, equilibrium, bifurcation, mass action, spring mass, limit cycles.This is a very rich set of notes, rich in examples and ideas for modeling. In...

3101SSpringMassFirstTry
22 Jul 2016   Contributor(s):: Keith Alan Landry, Brian Winkel

3060SDataToDifferentialEquation
24 Dec 2015   Contributor(s):: Eric Sullivan, Kelly Cline
Students use their knowledge of secondorder linear differential equations in conjunction with physical intuition of springmass systems to estimate the damping coefficient and spring constant from data. The data is presented as {%5Cit total distance traveled} instead of displacement so the...

1011ASKinetics
06 Jun 2015   Contributor(s):: Karen Bliss
Adapted from 111Kinetics, SIMIODE modeling scenario. We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and...

1019SRocksInTheHead
04 Jun 2015   Contributor(s):: Brian Winkel
We describe an experiment and offer data from a previously conducted experiment on the perception of the individual mass of a collection of rocks in comparison to a 100 g brass mass. We lead students to use the logistic differential equation as a reasonable model, estimate the parameters,...

1011SKinetics
03 Jun 2015   Contributor(s):: Brian Winkel
We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We offer many opportunities to model these chemical reactions with data, some of which comes from...