
3105SFrequencyResponse
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.

3034TCarSuspensions
14 Jul 2020   Contributor(s):: Therese Shelton, Brian Winkel
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   Contributor(s):: Therese Shelton, Brian Winkel
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   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.

3026SSpringInverseProblem
29 May 2020   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.

3031SSpringCost
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.

Transient and Steady State response in RC or RL circuits
16 Apr 2020   Contributor(s):: Brian Winkel
Transient and Steady State response in RC or RL circuits . PowerPoint Slides. 54 Slides, This is a presentation to help understand the concepts of Transient and Steady State response in RC or RL circuits . There is detailed technical material and graphs to richly illustrate the clear...

2013SuttonSecondOrderLinearODE'sPartII
27 Mar 2020   Contributor(s):: Brian Winkel
2013SuttonSecondOrderLinearODE'sPartIIPresentation by Craig J. Sutton, Department of Mathematics, Dartmouth CollegeMath 23 Differential Equations. 2013. 45 slidesCovers basics or undetermined coefficiens and variation of parameters with applications to mechanicl vibrations

2011CasaXPSMechanics ApplicationsDEs
20 Mar 2020   Contributor(s):: Brian Winkel
2011CasaXPSMechanics ApplicationsDEsCasaXPS. 2011 Variable Forces and Differential Equations. www.casaxps.com. Table of ContentsVariable Forces and Differential Equations 2Differential Equations 3Second Order Linear Differential...

2012EhrkeSecondOrderEquationsThreeCases
20 Mar 2020   Contributor(s):: Brian Winkel
2012EhrkeSecondOrderEquationsThreeCasesEhrke, John. 2012. Second Order Equations, Three Cases. Presentation 17 slides.Presentation on the three possible cases corresponding to possible eigenvalues from characteristic equation. nic and concise.

2008SanAndresDynamicResponseSecondOrderMechanicalSystems
16 Mar 2020   Contributor(s):: Brian Winkel
2008SanAndresDynamicResponseSecondOrderMechanicalSystemsSan Andrés, Luis. 2008. Dynamic Response of Second Order Mechanical Systems with Viscous Response Forces. MEEN 617 NotesPresentation. 39 pp.Walk through the cases in context of second order linear constant...

3150SItsABlastFurnace
13 Aug 2019   Contributor(s):: Kurt Bryan
This project uses the steadystate heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.The heat flow is assumed to be steadystate, so that only an elementary ordinary differential equation (ODE) is needed, and...

5005TextSStiffDifferentialEquations
05 Mar 2019   Contributor(s):: Kurt Bryan
This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples.Stiffness is a property that a system of ODE's may possess that make it difficult to solve numerically with standard methods, and it is a...

Farley and Tiffany  Time to Change our Traditional Differential Equations
19 Jan 2018   Contributor(s):: Patrice Geary Tiffany, Rosemary Carroll Farley
Time to Change our Traditional Differential Equations By Rosemary Farley and Patrice Tiffany, Manhattan College.A talk given at the AMS Special Session on Modeling in Differential Equations  High School, TwoYear College, FourYear Institution at Joint Mathematics Meetings, San Diego...

2015EndaleApplicationsOfODEsToRealWorldSystems
26 Nov 2017   Contributor(s):: Brian Winkel
2015. Endale, Mersha Amdie. Some application of first order differential equations to real world system. Masters Thesis. Haramaya University.We quote from the opening by the author,“The subject of differential equations is important part of mathematics for understanding the physical...

2011HarwoodModeling a RLC Circuit
12 Sep 2017   Contributor(s):: Brian Winkel
Harwood, Kenny. 2011. Modeling a RLC Circuit’s Current with Differential Equations. Paper. 17 pp.Abstract The world of electricity and light have only within the past century been explained in mathematical terms yet still remain a mystery to the human race. R. Buckminster Fuller said;...

2009MallettFetbrandtDifferential Equations Class Notes
11 Sep 2017   Contributor(s):: Brian Winkel
Mallett, Travis and Josh Fetbrandt. Differential Equations Class Notes. Washington State University.From the Dear Reader opening page of these notes,“These notes were written by two students (Travis Mallett and Josh Fetbrandt) at Washington State University in Fall 2009 and are intended to...

2015PendrillEagerTrampoline Jumping Model
09 Sep 2017   Contributor(s):: Brian Winkel
Pendrill. AnnMarie and David Eager. 2015. Free fall and harmonic oscillations: analyzing trampoline jumps. Physics Education. 50(1): 19.http://iopscience.iop.org/article/10.1088/00319120/50/1/64/meta . Accessed 5 September 2017. (This is an authorcreated, uncopyedited version of an...

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,...

2017DomokosDifferential Equations Theory and Applications Notes
07 Sep 2017   Contributor(s):: Andras Domokos
Domokos , Andras. 2017. Differential Equations  Theory and Applications – Notes. 126 pp. California State University, Sacramento. http://www.csus.edu/indiv/d/domokos/diffeq.pdf . Accessed 6 September 2017.The author says in the Introduction,“Differential Equations is a...