3-054-Relay-ModelingScenario

20 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/TMFG-Y761

We use a differential equations of one dimensional projectile motion and an integration of velocity for total distance to model the relay between an outfielder and an infielder in throwing the ball to home plate.

3-075-RLCCircuits-ModelingScenario

19 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/3BXJ-N820

We introduce the basics of RLC circuits, defining the terms of inductance, resistance, and capacitance in a circuit in which an induced voltage created a current running through these devices.

1-001-MM-DeathAndImmigration-ModelingScenario

19 May 2022 | 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

3-101-SpringMassFirstTry-NoResistance-ModelingScenario

19 May 2022 | 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.

3-102-SpringMassDamped-ModelingScenario

19 May 2022 | 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.

3-140-TwoSpringsOneMassFixedEnds-ModelingScenario

19 May 2022 | 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.

5-010-DNADegradation-ModelingScenario

18 May 2022 | 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.

5-011-ModelingIbuprofren-ModelingScenario

18 May 2022 | 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.

5-012-LipoproteinModeling-ModelingScenario

18 May 2022 | 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.

5-014-TwoSpringMass-ModelingScenario

18 May 2022 | 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.

5-022-ColdPill-ModelingScenario

18 May 2022 | 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.

5-023-FakingGause-ModelingScenario

18 May 2022 | 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.

5-025-SaltCompartments-ModelingScenario

18 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/5229-S610

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

5-030-AirshedSulphur-ModelingScenario

18 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/XCQ4-KA57

Temperature inversions and low wind speeds trap air pollutants in a mountain valley for a period of time. Gaseous sulfur compounds are a significant air pollution problem. We offer a model for analysis to predict long-term levels of levels of polutants.

5-040-TunedMassDampers-PartII-ModelingScenario

18 May 2022 | Contributor(s): Keith Landry, Brian Winkel | doi:10.25334/0B0A-QD10

Studentsbuild mathematical models to mitigate dangerous swaying in structures using structural improvements called Tuned Mass Dampers (TMD). We model the motion of the original structure as a spring-mass-dashpot with stiffness replacing spring constant.

6-004-VillageEpidemic-ModelingScenario

18 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/BKAC-X775

Students are offered data from a plague epidemic that occurred in the middle of the seventeenth century in Eyam, a small English village. With only two assumptions offered to students they are to build a mathematical model.

6-012-RiverCrossing-ModelingScenario

17 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/T7ZA-NX19

Students develop a model of a river crossing in a boat with thrust using Newton's Second Law of Motion from a Free Body Diagram they construct. The model is thence a system of one second order linear and a second order nonlinear differential equations.

6-019-EnablingEpidemicExploration-ModelingScenario

17 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/6VZ9-QX91

We became aware of several interesting possibilities for a modeling opportunity with data and we invited you to explore the several routes to parameter estimation in a SIR model with respect to the data offered.

6-030-SaltAndTorricelli-ModelingScenario

17 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/ZWP7-B233

We build on a model for the height of a falling column of water with a small hole in the container at the bottom of the column of water. We use data from one video of a falling column of water.

6-035-Shampoo-ModelingScenario

17 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/A6FK-B412

We ask students to model the amount of shampoo in a bottle if when we shower we do not cover the opening at the top of the bottle while in the shower.

3-080-PendulumModeling-ModelingScenario

16 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/W8PT-ZA09

We lead students through building model for several pendulum configurations in motion and ask students to compare results.

1-009-ICUSpread-ModelingScenario

16 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/MW29-FF80

We offer students the opportunity to model the percentage of voluntary nonprofit hospitals in the United States with Intensive Care Units during the period of 1958-1974.

1-008-HangTime-ModelingScenario

18 Jun 2022 | Contributor(s): Brian Winkel | doi:10.25334/R00Q-AY25

We present a modeling opportunity for students in which they model the vertical position of a basketball player taking a jump shot. The goal of the scenario is to get students to consider the meaning of the notion ``hang-tune.''

1-004-MicroorganismImmigration-ModelingScenario

15 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/SE0M-2X66

We present a modeling opportunity for population death with non-constant immigration and suggest the use of both discrete and continuous models with a comparison of results.

6-028-SaltCompartments-ModelingScenario

09 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/JS7V-GE02

Model a phenomena in which salt mixtures from two tanks are mixed with changing volumes of water.