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  1. 3-009-S-BallDropInWater

    16 Dec 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.

  2. 2008-Will-Hansen-ExamplesOfODEsInPhysics

    09 Dec 2018 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Witt-Hansen, Ole. 2008. Examples of the Differential equations of Physics. www.olewitthansen.dk. Contents1. The dependence of pressure with altitude.............................................................................. 12. Radioaktive chains of decay...

  3. 2004-PhoebusReily-TheParachuteProblem

    09 Dec 2018 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Phoebus, Ronald and Cole Reilly. 2004, Differential Equations and the Parachute Problem. Presentation 10 May 2004.  https://mse.redwoods.edu/darnold/math55/DEproj/sp04/coleron/presentation.pdf .Abstract: The parachute problem is a classical first semester differential equations problem...

  4. Modeling Falling Bodies

    01 Mar 2018 | Articles and Publications | Contributor(s): Hans Rudolf Schneebeli

    Modelling falling bodies is discussed using a computer algebra system-calculator and introducing various traditional and elementary methods from calculus as well as  numerics for dealing with the resulting ordinary differential equations.This article is in German under the title,...

  5. Pretty Good Physics

    13 Nov 2017 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    We were introduced to PrettyGood Physics  by a high school physics teacher colleague, Paul Beeken, Physics, Byram Hills High School, Armonk NY USA.  He has posted some very nice materials there on differential equations. All the material at this website is free and...

  6. 2006-LoydWodarz Drug Resistance in Acute Viral Infections

    18 Sep 2017 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Loyd, Alun L. and Dominik Wodarz.  2006. Drug Resistance in Acute Viral Infections:  Rhinovirus as a Case Study.  Preprint. 21 pp. http://www4.ncsu.edu/~allloyd/pdf_files/resistance_preprint.pdf . Accessed 18 September 2017.Abstract:  The emergence and spread of drug...

  7. 1994-Minton-Progression of Projectiles - Examples from Sports

    12 Sep 2017 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Minton, Roland. 1994. A Progression of Projectiles - Examples from Sports. The College Mathematics Teacher. 28(5): 436-442.There is a progression of complexity and issues in projectile motion modeling from no rsistance, to resistance proportional to velocity, then to velocity...

  8. Math Modeling with Differential Equations - Interesting Tank Problem

    12 Sep 2017 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Math Modeling with Differential Equations - Interesting Tank ProblemMath Modeling with Differential Equations - Interesting Tank Problem . Class Notes on five problems.,Several models are workd out including exponential decay, bullet traveling with resisitance, This material contains a solution...

  9. Calculus for Engineers II-Sample Problems on mathematical modeling with differential equations

    10 Sep 2017 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Calculus for Engineers II-Sample Problems on mathematical modeling with differential equations. https://www.maths.tcd.ie/~manuela/Sample_1.pdf . Accessed 10 September 2017.Five modeling activities involved with emptying various tanks, projectile motion with resistance, and population growth and...

  10. 2017-Groetsch-HammerANDFeather

    09 Sep 2017 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Groetsch, C. W. 2017. Hammer and Feather:  Some Calculus of Mass and Fall Time. Mathematics Magazine. 90: 3-7.The paper opens this way,“Does a heavy object fall faster than a lighter one? In 1971 NASA astronaut Dave Scott, Commander of the Apollo 15 lunar mission, used a hammer and a...

  11. 3-075-S-RLCCircuit

    17 May 2017 | Modeling Scenarios | Contributor(s): Brian Winkel

    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.

  12. What Goes Up Must Come Down

    02 Mar 2017 | Articles and Publications | Contributor(s): Brian Winkel

    Brauer, F. 1999. What Goes Up Must Come Down. American Mathematical Monthly. 108(5): 437-440.Article Abstract: NONEThis paper is a wonderfully general analysis of the following, “It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum height...

  13. Terminal velocity of a shuttlecock in vertical fall

    01 Mar 2017 | Articles and Publications | Contributor(s): Brian Winkel

    Peastrel, M., R. Lynch, and A. Armenti, Jr. 1980. Terminal velocity of a shuttlecock in vertical fall. American Journal of Physics. 48(7): 511-513.Article Abstract: We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are important and...

  14. Balloon Experiment in the Classroom

    01 Mar 2017 | Articles and Publications | Contributor(s): Brian Winkel

    Gruszka, T. 1994. A Balloon Experiment in the Classroom. The College Mathematics Journal. 25(5): 442-444.We quote from the article,“The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick. . . . The goals of the experiment include fostering...

  15. 3-065-S-UpDown

    05 Oct 2016 | Modeling Scenarios | Contributor(s): Brian Winkel

  16. 1999Brauer What Goes Up Must Come Down

    20 Jun 2015 | Potential Scenario Ideas | Contributor(s): F. Brauer

    Article Review and AnnotationBrauer, F. 1999.  What Goes Up Must Come Down.  American Mathematical Monthly. 108(5):  437-440.This paper is a wonderfully general analysis of the following, “It is natural to ask whether a particle propelled upwards takes longer to fall to...

  17. 1999MeadeStruthers Parachute Problem

    20 Jun 2015 | Potential Scenario Ideas | Contributor(s): Douglas B. Meade, Allan A. Struthers

    Meade, Douglas B. and Allan A. Struthers. 1999. Differential Equations in the New Millennium:  The Parachute Problem. International Journal of Engineering Education.  15(6): 417-424.Article Abstract: Introductory courses in differential equations have traditionally consisted of a long...

  18. 1994Gruszka Modeling falling balloon - experiment and analysis

    20 Jun 2015 | Potential Scenario Ideas | Contributor(s): T. Gruszka

    Gruszka, T. 1994. A Balloon Experiment in the Classroom. The College Mathematics Journal. 25(5): 442-444.We quote from the article,“The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick. . . .  The goals of the experiment include...

  19. 1980-Peastrel-Terminal velocity of a shuttlecock

    20 Jun 2015 | Potential Scenario Ideas | Contributor(s): M. Peastrel, R. Lynch, A. Armenti, A. Armenti Jr.

    Peastrel, M., R. Lynch Lynch, and A.Armenti, Jr. 1980. Terminal velocity of a shuttlecock in vertical fall. American Journal of Physics. 48(7): 511-513.Article Abstract:  We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are...

  20. 3-013-S-WhiffleBallFall

    30 May 2015 | Modeling Scenarios | Contributor(s): Brian Winkel

    We are given data on the time and position of a whiffle ball as it falls to the ground. We attempt to model the falling ball and we confront the different resistance terms and models. Finally, we introduce a new way of comparing models, the Akaike Information Criterion, and apply it to our models.