1. 3-090-OneSpringMass-ModelingScenario


    2022-05-20 01:46:08 | Teaching Materials | Contributor(s): Eric Ahlstrom, Swarn Singh, John Sieben, Tiernan Fogarty, John Thoo | doi:10.25334/TBGB-TA07

    We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their model to approximate the value of the spring constant.

  2. 1-001-MM-DeathAndImmigration-ModelingScenario


    2022-05-19 23:14:38 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/681Y-V837

    We describe a classroom activity in which students use M&M candies to simulate death and immigration. Students build a mathematical model, usually a linear first order, difference or differential equation, collect data, estimate parameters, and compare t

  3. 3-091-SpringModeling-ModelingScenario


    2022-05-19 18:40:24 | Teaching Materials | Contributor(s): Bonnie Moon | doi:10.25334/ZVTR-SY62

    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.

  4. 3-092-WirelessPower-ModelingScenario


    2022-05-19 19:48:39 | Teaching Materials | Contributor(s): Iordanka Panayotova, Maila Hallare | doi:10.25334/P8WT-3E63

    We present an engineering application (wireless power transmission) modelled by a coupled system of two linear second-order differential equations with constant coefficients. One equation is homogeneous while the other one is non-homogeneous.

  5. 3-101-SpringMassFirstTry-NoResistance-ModelingScenario


    2022-05-19 19:51:37 | Teaching Materials | Contributor(s): Keith Landry, Brian Winkel | doi:10.25334/Z3KB-A454

    Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with no damping.

  6. 3-102-SpringMassDamped-ModelingScenario


    2022-05-19 19:55:18 | Teaching Materials | Contributor(s): Keith Landry, Brian Winkel | doi:10.25334/42BV-E297

    Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with damping.

  7. 3-130-MatterOfSomeGravity-ModelingScenario


    2022-05-19 19:56:22 | Teaching Materials | Contributor(s): Kurt Bryan | doi:10.25334/RN52-2M43

    This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.

  8. 3-140-TwoSpringsOneMassFixedEnds-ModelingScenario


    2022-05-19 19:57:19 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/D8NG-S248

    Students build a model of a two spring, single mass with fixed end configuration and then plot solutions to experience the motion.

  9. 4-020-AnIEDBlast-ModelingScenario


    2022-05-19 19:58:02 | Teaching Materials | Contributor(s): Jonathan Paynter, George Hughbanks | doi:10.25334/VEHT-G707

    These three exercises offer students a chance to model with second order ordinary differential equations, how they might incorporate a spring-mass system into a larger model, and how they can use the model to determine the results of a dynamical sysstem.

  10. 4-036-AltitudeDependentGravity-ModelingScenario


    2022-05-19 19:58:56 | Teaching Materials | Contributor(s): Jakob Kotas | doi:10.25334/031Y-V406

    When projectiles are way above Earth's surface gravity's changes become important when dealing with projectiles at high altitudes. We lay out an approach for such a case which is a second-order differential equation.

  11. 4-039-FallingDarts-ModelingScenario


    2022-05-19 19:59:46 | Teaching Materials | Contributor(s): Jacob Duncan | doi:10.25334/DKQK-YS87

    we develop, solve, and analyze a second order differential equation model for free fall incorporating air resistance. Students solve the model using two methods -- reduction of order and separation of variables, and method of undetermined coefficients.

  12. 4-065-GasInjection-ModelingScenario


    2022-05-19 20:00:27 | Teaching Materials | Contributor(s): Vladimir Riabov | doi:10.25334/9QG8-MP36

    Students use programs (or create their own code) based on exponential box-scheme approximations for solving systems of nonlinear differential equations that contain small parameters for the highest derivative terms or singularities in boundary conditions.

  13. 5-010-DNADegradation-ModelingScenario


    2022-05-19 20:01:58 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/YK0G-N372

    We ask students to use the system of first order linear differential equations given in a source paper and estimates of the data from laboratory procedures from a plot to estimate the parameters and complete the modeling process.

  14. 5-011-ModelingIbuprofren-ModelingScenario


    2022-05-19 20:02:43 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/9KNF-6460

    We consider modeling of data from a clinical experiment administered as oral doses of 400 mg ibuprofen, an analgesic pain reliever. Concentrations of ibuprofen in the serum/plasma of the subjects were recorded after the initial ingestion of the drug.

  15. 5-012-LipoproteinModeling-ModelingScenario


    2022-05-19 20:03:30 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/1163-6J70

    Data from a study on the amounts of low-density-lipoprotein (LDL), form of cholesterol, in blood plasma is presented. Students build, validate, and use a compartment model of the kinetic exchange of the LDL between body tissue and blood plasma.

  16. 5-014-TwoSpringMass-ModelingScenario


    2022-05-19 20:04:22 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/4CY9-QP25

    We ask students to build a Free Body Diagram for a vertical two mass situation in which the two masses are held fixed at the tip and at the bottom. The mass holds the springs together at the join of the two springs in between.

  17. 5-015-RunnersSynchronize-ModelingScenario


    2022-05-19 20:01:12 | Teaching Materials | Contributor(s): Eli Goldwyn | doi:10.25334/TF3Z-0556

    In this modeling scenario we practice finding and classifying equilibria of a one-variable differential equation. We do this in the context of a phase model which is often a simpler way of studying oscillatory phenomena.

  18. 5-022-ColdPill-ModelingScenario


    2022-05-19 20:05:09 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/EEYW-QZ48

    A model for the flow of a cold pill drug through the gastrointestinal compartment to the bloodstream compartment of a human subject is proposed. Students solve the system of differential equation model, use known parameter values, and plot solutions.

  19. 5-023-FakingGause-ModelingScenario


    2022-05-19 20:05:47 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/TRPR-KT70

    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 competition in the 1930's studies of G. F. Gause in the Soviet Union.

  20. 5-025-SaltCompartments-ModelingScenario


    2022-05-19 20:07:24 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/5229-S610

    Model a phenomena in which salt mixtures from two tanks are mixed using several strategies.