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3-105-S-FrequencyResponse
22 Jul 2020 | Modeling Scenarios | Contributor(s):: Brian Winkel
We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.
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3-034-S-CarSuspensions
14 Jul 2020 | Modeling Scenarios | Contributor(s):: Therese Shelton, Brian Winkel
We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a "quarter car'', meaning a single wheel.
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3-027-S-BobbingDropping
10 Jul 2020 | Modeling Scenarios | Contributor(s):: Brian Winkel
We present two exercises from a differential equations text in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.
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1-088-S-RoomTemperature
15 Jun 2020 | Modeling Scenarios | Contributor(s):: Tracy Weyand
Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken). The main goal of this project is for students to set up...
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1-136-S-MarriageAge
11 Jun 2020 | Modeling Scenarios | Contributor(s):: Tracy Weyand
Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. This model comes from a paper by Hernes and, in this project, is compared to another model used by Coale.These models are first-order ordinary differential equations (which...
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1-128-S-RocketFlight
04 Jun 2020 | Modeling Scenarios | 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.
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1-124-S-WorldPopulation
30 May 2020 | Modeling Scenarios | Contributor(s):: Lenka Pribylova, Jan Sevcik, Pavel Morcinek, Brian Winkel
We build models of world population using data to estimate growth rate.CZECH LANGUAGE VERSION We have placed in Supporting Docs a Czech version of this Student Modeling Scenario. Name will be x-y-S-Title-StudentVersion-Czech.
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3-026-S-SpringInverseProblem
29 May 2020 | Modeling Scenarios | 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.
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3-031-S-SpringCost
28 May 2020 | Modeling Scenarios | Contributor(s):: Brian Winkel
This is a situation where we are charged with analyzing costs for a spring to meet certain specifications.
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6-016-S-PandemicModeling
13 May 2020 | Modeling Scenarios | Contributor(s):: Jue Wang
The recent coronavirus outbreak has infected millions of people worldwide and spread to over 200 countries. The virus is spreading rapidly. Infectious disease modeling is an essential part of the effort to minimize the spread and help predict the likely course of an epidemic. How can we use...
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1-127-S-FishHarvesting-StudentVersion
06 May 2020 | Modeling Scenarios | Contributor(s):: Will Mitchell
We offer students a harvesting model for operating a fishery over a 25 year horizon and ask them to write a report on optimal harvesting policy with their analyses for fishing industry experts (not necessarily mathematicians).
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5-010-S-DNADegradation
21 Apr 2020 | Modeling Scenarios | Contributor(s):: Brian Winkel
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. Then we seek to compare the results of the final model with...
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6-009-S-FakeNews
19 Apr 2020 | Modeling Scenarios | Contributor(s):: Sarah Elizabeth Ritchey Patterson, Blain Patterson
In modern society, creating and disseminating information is easier than ever. While this allows access to information on unprecedented scales, the validity of the information can be difficult to determine. Clickbait, propaganda, misleading headlines, biased news outlets, and social media posts...
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6-045-S-CholeraTranmission
19 Apr 2020 | Modeling Scenarios | Contributor(s):: Urmi Ghosh-Dastidar
A recent cholera outbreak in Haiti brought public attention to this disease. Cholera, a diarrheal disease, is caused by an intestinal bacterium, and if not addressed in a timely manner may become fatal. During the project described here, the students will learn how to solve and address a...
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1-126-S-MarriageMath
14 Apr 2020 | Modeling Scenarios | Contributor(s):: Erdi KARA
We will explore a model which describes the process of entry into marriage by an individual. In the model, rate of change in the fraction of the cohort already married will be investigated along with two governing assumptions; social pressure experienced by unmarried individual increases as...
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3-015-S-StyrofoamBallFall
24 Mar 2020 | Modeling Scenarios | Contributor(s):: Brian Winkel
We are given data on a falling Styrofoam ball and we seek to model this motion.
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3-063-S-FallingBuildingIce
07 Mar 2020 | Modeling Scenarios | Contributor(s):: Brian Winkel
We model the fall of a piece of ice which is falling from a high building in New York City.
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5-077-S-MandMAttritionWarfare
23 Feb 2020 | Modeling Scenarios | Contributor(s):: Lukasz Grabarek
Students will model attrition between two opposing forces using m&m candies. Through experiment and data collection, students will determine the parameters describing the fighting strength of each force, solve the system, arrive at Lanchester's N-square Law and use it to analyze a...
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5-015-S-RunnerSynchronize
13 Jan 2020 | Modeling Scenarios | Contributor(s):: Eli E Goldwyn
The goal is for students to practice finding and classifying equilibria of a one-variable system in this modeling context while also introducing variables defined on a restricted domain (the circle).
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1-116-S-TropicalStormWindspeeds
12 Jan 2020 | Modeling Scenarios | Contributor(s):: Terrance Pendleton
We model the decay of tropical cyclone winds once a storm makes landfall. We use data from two recent storms from the National Hurricane Center to estimate parameters emanating from a differential equation model.