
7020SThermometerInVaryingTempStream
22 Aug 2018   Contributor(s):: Norman Loney
We present a differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.

4055SShatterWineGlass
20 Aug 2018   Contributor(s):: Jue Wang
This module takes students through real life scenarios to examine resonance and its destructive power using differential equation models. What is resonance? How does it happen? Why is it important? Three cases are presented: shattering a wine glass, collapse of a suspension bridge, and crash of...

2008WitthansenExamplesOfDifferentialEquationsInPhysics
28 Nov 2017   Contributor(s):: Brian Winkel
WittHansen, Ole. Examples Of Differential Equations In Physics. Article. 29 pp. Source: www.olewitthansen.dk . Accessed 27 November 2017.This is an article from the author’s homepage. The work contains fundamental and basic background and derivation of the differential equation...

MorinOsillations
11 Sep 2017   Contributor(s):: Brian Winkel
Morin, David. Oscillations. http://www.people.fas.harvard.edu/~djmorin/waves/oscillations.pdf . Accessed 11 September 2017. Notes. 37 pp.From the first page“A wave is a correlated collection of oscillations. For example, in a transverse wave traveling along a string, each point in the...

2011ShibberuDEClassNotes
09 Sep 2017   Contributor(s):: Brian Winkel
Shibberu, Yosi. 2011. MA211 Differential Equations. Class Notes. PowerPoint. 426 slides. https://www.rosehulman.edu/~shibberu/MA211/Slides.pdf . Accessed 1 September 2017 This is a very good set of course slides and the Table of Contents is given here. Since this is a mathematics...

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,...

2003FayGrahamCoupledSpringEquations
08 Sep 2017   Contributor(s):: Brian Winkel
Fay, T.H. and S. D. Graham. 2003. Coupled spring equations. Int.J. Math. Educ. Sci. Technol. 34(1): 6579. ABSTRACT Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described. For the linear model...

1967Isrealsson JohnssonCircumnutations In Helianthus Annuus
08 Sep 2017   Contributor(s):: Brian Winkel
Israelsson, D. and A. Johnsson. 1967. A Theory for Circumnutations in Helianthus annuus. Physiologia Plantarum. 20: 957976.Abstract:“A theory is given for circumnutations in plants, especially hypocotyls of Helianthus annuus, which were used as experimental material.“The...

1969JohnssonIsraelssonPhase Shift In Geotropical Oscillations
08 Sep 2017   Contributor(s):: Brian Winkel
Israelsson, D. and A. Johnsson. 1969. Phaseshift in Geotropic Oscillations a Theoretical and Experimental Study. Physiologia Plantarum. 22: 12261237.The paper studies geotropical induced phaseshifts in circumnutations (turning) of Helianthus annus hypocotlys. Theory based on...

HELMWorkbook19Differential_Equations
05 Sep 2017   Contributor(s):: Brian Winkel
HELM. Workbook 19: Differential Equations. 74 pp. From site http://helm.lboro.ac.uk/Over 50 workbooks are freely available for download a the site. This workbook Workbook 19: Differential equations is a nice mix of examples worked out concerning skills and models. The...

1043SCoolingUpAndDown
26 Aug 2017   Contributor(s):: Brian Winkel
We consider modeling the attempt of an air conditioner to cool a room to a ``constant'' temperature.

3101SSpringMassFirstTry
22 Jul 2016   Contributor(s):: Keith Alan Landry, Brian Winkel

1977MackeyGlassOscillation and Chaos in Physiological Control Systems
26 Jun 2015   Contributor(s):: Michael C. Mackey, Leon Glass, William Clark
Mackey, Michael C. and Leon Glass. 1977. Oscillation and Chaos in Physiological Control Systems. Science. 197: 287289.Article Abstract: Firstorder nonlinear differentialdelay equations describing physiological control systems are studied. The equations display a broad diversity of...

9012SPDEGuitarTuning
04 Jun 2015   Contributor(s):: Brian Winkel
We present a derivation of a partial differential equation which models the motion of a string held at both ends, a case of the onedimensional wave equation. We immediately offer numerical solutions in a computer algebra system (we use Mathematica, but any...