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  1. 5-036-S-HalfCarVibration

    08 Aug 2021 | Modeling Scenarios | Contributor(s):: Shengyong Zhang

    Vibration vehicle models provide a great opportunity to integrate vehicle-based vibrations into a mechanical engineering vibrations course. This project works on a multiple-degree-of-freedom (MDOF) including the pitch and bounce of the vehicle body mounting on a suspension system. The approach...

  2. 1-134-S-LanguageDynamics

    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...

  3. 1-135-S-FishHarvesting

    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...

  4. 1-097-S-SwimmingPool

    08 Aug 2021 | Modeling Scenarios | Contributor(s):: Barbara Zubik-Kowal

    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...

  5. 6-067-S-LotkaVolterra

    07 Aug 2021 | Modeling Scenarios | Contributor(s):: Iordanka Panayotova, Maila Hallare

    This modeling scenario guides students through the process of fitting the Lotka-Volterra 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...

  6. 3-073-S-EarthQuake Part II

    06 Aug 2021 | Modeling Scenarios | Contributor(s):: Tracy Weyand

    This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring-damper system. In this activity, students will analyze motion of the roof under different damping and vibration...

  7. 3-072-S-EarthQuake Part I

    06 Aug 2021 | Modeling Scenarios | Contributor(s):: Tracy Weyand

    This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring system. In this activity, students will analyze the motion of the roof caused by ground movement. Here we...

  8. 3-092-S-WirelessPower

    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 second-order differential equations with constant coefficients. One of the equations is homogeneous while the other one is non-homogeneous. The application is called wireless power transmission...

  9. 6-029-S-TumorGrowth

    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...

  10. 1-150-S-CancerTherapy

    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...

  11. 6-017-S-OncolyticViruses

    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 virus-infected cancer cells y(t),  and the...

  12. 3-099-S-PullBack

    03 Aug 2021 | Modeling Scenarios | Contributor(s):: Brody Dylan Johnson

    This hands-on modeling scenario guides students through the development of an empirical model for the velocity and distance traveled of a simple pull-back toy. Students can record videos and extract data using their own pull-back toy or use data included in the student version. Two different...

  13. 5-076-S-LanchesterLaws

    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...

  14. 3-076-S-CircuitBuilding

    27 Jul 2021 | Modeling Scenarios | Contributor(s):: Chiu Choi

    In this project students will establish a mathematical model for an electric circuit as a second-order ordinary differential equation with constant coefficients. They will derive the initial conditions for this differential equation by using circuit laws. They will obtain its closed-form solution...

  15. 1-139-S-PlantsVsHerbivores

    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,...

  16. 1-137-S-SheepGraze

    03 Mar 2021 | Modeling Scenarios | Contributor(s):: Mary Vanderschoot

    One of the most well-known mathematical models in ecology is the Lotka-Volterra predator-prey 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...

  17. 6-026-S-FakingGause

    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.

  18. 1-119-S-DairyFarming

    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.

  19. 9-002-S-GroundWaterFlow

    31 Aug 2020 | Modeling Scenarios | Contributor(s):: Jeremy Cristman, Kenneth Luther, Michael Karls

    The goals of this project are to compare a conceptual one-dimensional 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...

  20. 1-096-S-OpAmpDifferentiator

    09 Aug 2020 | Modeling Scenarios | Contributor(s):: Virgil Ganescu

    In this validation-oriented 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...