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Remote Teaching Module - Car Suspensions
28 Jul 2020 | | Contributor(s):: Therese Shelton
In this modeling activity, students examine the spring-mass-dashpot that is part of a car suspension. We model a "quarter car'', meaning a single wheel, and compare effects of different masses, spring constants, damping coefficients, and the angle at which the assembly is installed....
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3-105-S-FrequencyResponse
22 Jul 2020 | | 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-T-CarSuspensions
14 Jul 2020 | | Contributor(s):: Therese Shelton, Brian Winkel
In this modeling activity, students examine the spring-mass-dashpot that is part of a car suspension. We model a "quarter car'', meaning a single wheel, and compare effects of different masses, spring constants, damping coefficients, and the angle at which the assembly is...
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3-034-S-CarSuspensions
14 Jul 2020 | | 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 | | 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 | | 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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3-031-S-SpringCost
28 May 2020 | | 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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5-010-S-DNADegradation
21 Apr 2020 | | 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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2009-NoakeSleigh-AirflowInfectionHospitalWards
29 Mar 2020 | | Contributor(s):: Brian Winkel
2009-NoakeSleigh-AirflowInfectionHospitalWardsNoakes, Catherine J. and P. Andrew Sleigh. 2009. Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards. J. R. Soc. Interface. 6: S791-S-800.Abstract: Understanding the risk of...
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1-001d-S-HotelPopulationDecay
03 Jul 2019 | | Contributor(s):: Dina Yagodich
We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.
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3-067-S-RLCSeriesCircuit
28 Apr 2019 | | Contributor(s):: Virgil Ganescu
In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical model (using Multisim).
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7-011-Text-S-CoupledSystemLaplace
31 Mar 2019 | | Contributor(s):: Mitaxi Mehta
Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...
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1986-Cooke-Linear And Logistic Harvesting Models-Math Modeling Journal
09 Dec 2018 | | Contributor(s):: Brian Winkel
Cook, K. L. and M. Witten. 1986. One-dimensional linear and logistic harvesting models. Mathematical Modeling. 7: 301-340.Abstract: Some of the results in the literature on simple one-dimensional, density dependent, discrete and continuous models-with and without harvesting-are reviewed. Both...
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1-054-S-GrowthInFarmland
14 Aug 2018 | | Contributor(s):: Richard Spindler
An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...
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LeakingBucket: Differential Equations in Engineering
03 Mar 2018 | | Contributor(s):: Unknown
Differential Equations in Engineering: The Leaking Bucket. Laboratory Experiment. 4 pp.From the Text:7.1 Laboratory ObjectiveThe objective of this laboratory is to learn about first order differential equations and theirapplication to a leaking bucket. 7.2 Educational ObjectivesAfter...
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2003-RasmussenKeynes-LinesOfEigenVectorsSolutionsToSytemsOfLinearDifferentialEquations
03 Mar 2018 | | Contributor(s):: Chris Rasmussen, Michael Keynes
Rasmussen, Chris and Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations. PRIMUS. 13(4): 308-320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...
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1988-Strogatz-LoveAffairsAndDifferentialEquations
26 Nov 2017 | | Contributor(s):: Brian Winkel
Strogatz, Steven H. 1988. Love Affairs and Differential Equations. Mathematics Magazine. 61(7): 35.This is a system of differential equations to describe the love between Shakespeare’s Romeo and Juliet.Keywords: differential equation, system, linear, parameters
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2015-Easton-Mathematical models of health focusing on diabetes
11 Sep 2017 | | Contributor(s):: Brian Winkel
Easton, Jonathan. 2015. Mathematical models of health focusing on diabetes: Delay differential equations and data mining. Doctoral thesis, 186 pp. Northumbria University. http://nrl.northumbria.ac.uk/23582/ . Accessed 10 September 2017.This is an exhaustive study with very good...
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2013-Slavik-Mixing Problems with Many Tanks
10 Sep 2017 | | Contributor(s):: Brian Winkel
Slavik, Antonin. 2013. Mixing Problems with Many Tanks. Mathematics Monthly. 120: 806-821.Discusses many tank configurations, circular, cascading, in a row, etc. and the attendant matrix representation of the linear mixing model of differential equations. Keywords: tank, circula,...
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BobbingObjectInWater
09 Sep 2017 | | Contributor(s):: Brian Winkel
Introduction to Second Order Linear Equations- Bobbing Object in Water. 2 pp.This is a nice treatment of developing a model of a bobbing object in water from first principles with some nice additional questions which would make a nice Modeling Scenario.Keywords: buoyancy, bobbing, water,...