
5036SHalfCarVibration
08 Aug 2021  Modeling Scenarios  Contributor(s):: Shengyong Zhang
Vibration vehicle models provide a great opportunity to integrate vehiclebased vibrations into a mechanical engineering vibrations course. This project works on a multipledegreeoffreedom (MDOF) including the pitch and bounce of the vehicle body mounting on a suspension system. The approach...

1134SLanguageDynamics
08 Aug 2021  Modeling Scenarios  Contributor(s):: Jennifer Crodelle
Students will be introduced to a mathematical model for language dynamics. Specifically, the model describes the change in the fraction of a population speaking one language over another. By answering a list of questions, students will explore how changing the status of a language will alter the...

1135SFishHarvesting
08 Aug 2021  Modeling Scenarios  Contributor(s):: Jennifer Crodelle
This modeling scenario will introduce students to the concept of a bifurcation through a fish harvesting model. This short activity will walk students through a guided list of questions to help them to understand how the stability of equilibrium changes with changes in a model parameter, in this...

1097SSwimmingPool
08 Aug 2021  Modeling Scenarios  Contributor(s):: Barbara ZubikKowal
This project involves the dynamics of chlorine concentration during regular swimming pool maintenance cycles. Students will have the opportunity to use both analytic and numerical methods. On the analytical side, students will solve one of the model equations, describing the first stage of a...

6067SLotkaVolterra
07 Aug 2021  Modeling Scenarios  Contributor(s):: Iordanka Panayotova, Maila Hallare
This modeling scenario guides students through the process of fitting the LotkaVolterra model of two differential equations to a real time series observational data. Students use the capabilities of R and R studio, an integrated development environment for R, and the gauseR package, a collection...

3073SEarthQuake Part II
06 Aug 2021  Modeling Scenarios  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  Modeling Scenarios  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...

3092SWirelessPower
04 Aug 2021  Modeling Scenarios  Contributor(s):: Maila Hallare, Iordanka Panayotova
This activity presents an engineering application that is modelled by a coupled system of two linear secondorder differential equations with constant coefficients. One of the equations is homogeneous while the other one is nonhomogeneous. The application is called wireless power transmission...

6029STumorGrowth
04 Aug 2021  Modeling Scenarios  Contributor(s):: Allison Leigh Lewis
This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time. Students should have prior experience with solving ODEs using the separable...

1150SCancerTherapy
03 Aug 2021  Modeling Scenarios  Contributor(s):: Maila Hallare, Iordanka Panayotova
This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the other, surgery happens after therapy.Activities will help students appreciate the importance of...

6017SOncolyticViruses
03 Aug 2021  Modeling Scenarios  Contributor(s):: Iordanka Panayotova, Maila Hallare
In this project, students explore oncolytic virotherapy using systems of differential equations and numerical simulations. The first activity guides the students in simulating the dynamics between the uninfected cancer cells x(t), the oncolytic virusinfected cancer cells y(t), and the...

3099SPullBack
03 Aug 2021  Modeling Scenarios  Contributor(s):: Brody Dylan Johnson
This handson modeling scenario guides students through the development of an empirical model for the velocity and distance traveled of a simple pullback toy. Students can record videos and extract data using their own pullback toy or use data included in the student version. Two different...

5076SLanchesterLaws
27 Jul 2021  Modeling Scenarios  Contributor(s):: Blain Patterson
Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time, with the function depending only on A and B. In this project, you...

3076SCircuitBuilding
27 Jul 2021  Modeling Scenarios  Contributor(s):: Chiu Choi
In this project students will establish a mathematical model for an electric circuit as a secondorder ordinary differential equation with constant coefficients. They will derive the initial conditions for this differential equation by using circuit laws. They will obtain its closedform solution...

1139SPlantsVsHerbivores
08 Mar 2021  Modeling Scenarios  Contributor(s):: Mary Vanderschoot
In a recent study of plants and herbivores on an island in the North Sea, ecologists made a surprising observation: Instead of more vegetation resulting in more grazers, more vegetation resulted in fewer grazers. Consequently, the ecologists hypothesized that, as the vegetation grew more dense,...

1137SSheepGraze
03 Mar 2021  Modeling Scenarios  Contributor(s):: Mary Vanderschoot
One of the most wellknown mathematical models in ecology is the LotkaVolterra predatorprey system of differential equations. Initially, this model was used to analyze interactions between two animal populations. But ecologists discovered that it could also be applied to plant (`prey') and...

6026SFakingGause
30 Oct 2020  Modeling Scenarios  Contributor(s):: Brian Winkel
We use a fake or toy data set to permit discovery of the parameters in a two population protozoan model used to study paramecium and yeast competiton in the 1930's studies of G.~F.~Gause in the Soviet Union.

1119SDairyFarming
20 Sep 2020  Modeling Scenarios  Contributor(s):: Rob Krueger
A simple first order population growth model is presented. The challenge is to produce a final differential equation which is the result of the difference or ratio of birth and death rates. This ratio is not immediately intuitive.

9002SGroundWaterFlow
31 Aug 2020  Modeling Scenarios  Contributor(s):: Jeremy Cristman, Kenneth Luther, Michael Karls
The goals of this project are to compare a conceptual onedimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences. We derive the initial groundwater flow equation, and guide students through a solution. We describe the laboratory set up and...

1096SOpAmpDifferentiator
09 Aug 2020  Modeling Scenarios  Contributor(s):: Virgil Ganescu
In this validationoriented setup, the output waveform (function) of a operational amplifier type of differentiator circuit is determined analytically from the first order governing ordinary differential equation and the results are compared with the data acquired from analyzing the numerical...