
3105SFrequencyResponse
22 Jul 2020  Modeling Scenarios  Contributor(s): Karen Bliss
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.

3034TCarSuspensions
14 Jul 2020  Modeling Scenarios  Contributor(s): Karen Bliss
In this modeling activity, students examine the springmassdashpot 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...

3034TCarSuspensions
14 Jul 2020  Modeling Scenarios  Contributor(s): Karen Bliss
In this modeling activity, students examine the springmassdashpot 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...

3034SCarSuspensions
14 Jul 2020  Modeling Scenarios  Contributor(s): Karen Bliss
We examine the springmassdashpot 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.

3027SBobbingDropping
10 Jul 2020  Modeling Scenarios  Contributor(s): Karen Bliss
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.

1088SRoomTemperature
15 Jun 2020  Modeling Scenarios  Contributor(s): Karen Bliss
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...

3031SSpringCost
28 May 2020  Modeling Scenarios  Contributor(s): Karen Bliss
This is a situation where we are charged with analyzing costs for a spring to meet certain specifications.

5010SDNADegradation
21 Apr 2020  Modeling Scenarios  Contributor(s): Karen Bliss
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...

2009NoakeSleighAirflowInfectionHospitalWards
29 Mar 2020  Potential Scenario Ideas  Contributor(s): Karen Bliss
2009NoakeSleighAirflowInfectionHospitalWardsNoakes, 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: S791S800.Abstract: Understanding the risk of...

1001dSHotelPopulationDecay
03 Jul 2019  Modeling Scenarios  Contributor(s): Karen Bliss
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.

3067SRLCSeriesCircuit
28 Apr 2019  Modeling Scenarios  Contributor(s): Karen Bliss
In this validationoriented 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).

7011TextSCoupledSystemLaplace
31 Mar 2019  Technique Narratives  Contributor(s): Karen Bliss
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...

1986CookeLinear And Logistic Harvesting ModelsMath Modeling Journal
09 Dec 2018  Potential Scenario Ideas  Contributor(s): Karen Bliss
Cook, K. L. and M. Witten. 1986. Onedimensional linear and logistic harvesting models. Mathematical Modeling. 7: 301340.Abstract: Some of the results in the literature on simple onedimensional, density dependent, discrete and continuous modelswith and without harvestingare reviewed. Both...

1054SGrowthInFarmland
14 Aug 2018  Modeling Scenarios  Contributor(s): Karen Bliss
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...

LeakingBucket: Differential Equations in Engineering
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Karen Bliss
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...

2003RasmussenKeynesLinesOfEigenVectorsSolutionsToSytemsOfLinearDifferentialEquations
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Karen Bliss
Rasmussen, Chris and Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations. PRIMUS. 13(4): 308320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...

1988StrogatzLoveAffairsAndDifferentialEquations
26 Nov 2017  Potential Scenario Ideas  Contributor(s): Karen Bliss
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

2015EastonMathematical models of health focusing on diabetes
11 Sep 2017  Potential Scenario Ideas  Contributor(s): Karen Bliss
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...

2013SlavikMixing Problems with Many Tanks
10 Sep 2017  Potential Scenario Ideas  Contributor(s): Karen Bliss
Slavik, Antonin. 2013. Mixing Problems with Many Tanks. Mathematics Monthly. 120: 806821.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,...

BobbingObjectInWater
09 Sep 2017  Potential Scenario Ideas  Contributor(s): Karen Bliss
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,...