
2020Shelton, Therese  Remote Teaching Module  Car Suspensions
28 Jul 2020   Contributor(s):: Therese Shelton
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 installed....

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.

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.

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.

2020Zammit, Corey, Nirantha Balagopal, Zijun Li, Shenghao Xia, and Qisong Xiao  DynamicsOfElasticPendulum  Report
06 Apr 2020   Contributor(s):: Brian Winkel
Zammit, Corey, Nirantha Balagopal, Zijun Li, Shenghao Xia, and Qisong Xiao. THE DYNAMICS OF THE ELASTIC PENDULUMhttps://www.math.arizona.edu/~gabitov/teaching/141/math_485/Midterm_Reports/Elastic_pendulum_midterm_report.pdfThe system of the elastic pendulum consists of a spring, connected...

2014Cimbala, John M.  Dynamic System Response. Notes.
29 Mar 2020   Contributor(s):: Brian Winkel
Cimbala, John M. 2014. Dynamic System Response. Notes. 11 pages.See https://www.me.psu.edu/cimbala/me345/Lectures/Dynamic_systems.pdf .IntroductionIn an ideal world, sensors respond instantly to changes in the parameter being measured.In the real world, however,...

2013I. Boscolo, F. Castelli, and M. Stellato  An undergraduate study of harmonic and parametric motion of a simple springmass system from motion waveforms.
20 Mar 2020   Contributor(s):: Brian Winkel
I. Boscolo, F. Castelli, and M. Stellato. 2013. An undergraduate study of harmonic and parametric motion of asimple springmass system from motion waveforms. Dipartimento di Fisica, Universit`a degli Studi di Milano. 17 pp.See https://arxiv.org/pdf/1208.1126.pdf...

1989Blickhan, R.  Spring Mass Model For RunningHopping.
13 Mar 2020   Contributor(s):: Brian Winkel
Blickhan, R. 1989. Spring Mass Model For RunningHopping. J. Biomechanics. 22(11/12): 12171227.See https://www.cs.cmu.edu/~hgeyer/Teaching/R16899B/Papers/Blickhan89JBiom.pdf .Abstract: A simple spring—mass model consisting of a massless spring attached to a point mass...

2003Givens, Ryan and O. F. de Alcantara Bonfima  Direct observation of normal modes in coupled oscillators.
13 Mar 2020   Contributor(s):: Brian Winkel
Givens, Ryan and O. F. de Alcantara Bonfima. 2003. Direct observation of normal modes in coupled oscillators. From Physics Commons. See https://pilotscholars.up.edu/phy_facpubs/6/. Abstract: We propose a simple and inexpensive method to directly...

2007Bellomo, Nicola , Elena De Angelis, and Marcello Delitala  Lecture Notes on Mathematical Modelling in Applied Sciences
03 Mar 2018   Contributor(s):: Nicola Bellomo
Bellomo, Nicola , Elena De Angelis, and Marcello Delitala. 2007. Lecture Notes on Mathematical Modelling in Applied Sciences, Lecture Notes. 168 pp.See https://staff.polito.it/marcello.delitala/dwd/mechanic_Simai.pdf .From the Opening of the Notes:The Lecture Notes...

2018Farley, Rosemary and Patrice 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,...

2018Theodosopoulos, Ted  Modeling Challenges for a High School Course on Differential Equations
19 Jan 2018   Contributor(s):: Ted Theodosopoulos
Modeling Challenges for a High School Course on Differential EquationsBy Ted Theodosopoulos, The Nueva School.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...

2012Rusinko, Joseph and Hannah Swan  AgentBased Fabric Modeling Using Differential Equations.
11 Sep 2017   Contributor(s):: Brian Winkel
Rusinko, Joseph and Hannah Swan. 2012. AgentBased Fabric Modeling Using Differential Equations. CODEE Journal. 9(1):112.See http://scholarship.claremont.edu/codee/vol9/iss1/7/ . Accessed 10 September 2017.Abstract: We use an agentbased modeling software, NetLogo, to simulate...

2011Shibberu, Yosi  MA211 Differential Equations. Class Notes
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 2017This is a very good set of course slides and the Table of Contents is given here. Since this is a mathematics...

2003Fay, T.H. and S. D. Graham  Coupled spring equations.
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. See https://www.tandfonline.com/doi/abs/10.1080/0020739021000029258 . ABSTRACT Coupled spring equations for modelling the motion of two springs with...

2017Stan, GuyBart  Modelling in Biology.
02 Sep 2017   Contributor(s):: Brian Winkel
2017. Stan, GuyBart. Modelling in Biology. Class Notes. Imperial College of London. 71 pp.Keywords: differential equation, model, stability, equilibrium, bifurcation, mass action, spring mass, limit cycles.This is a very rich set of notes, rich in examples and ideas for modeling. In...

3040SFirstPassageTime
07 Apr 2017   Contributor(s):: Brian Winkel
We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time with several applications.

3002SModelsMotivatingSecondOrder
30 Mar 2017   Contributor(s):: Brian Winkel
We introduce several basic, but substantial, approaches to modeling the motion of a spring mass system using a standard second order, linear, constant coefficient differential equation obtained from Newton's Second Law of Motion and a Free Body Diagram. We do this using a set of data...

3110SMilitarySpringMassApplication
25 Feb 2017   Contributor(s):: Randy Boucher, Ivan Dungan
The project is a collection of five different scenarios regarding the shock system of a trailer; the first three are chronological and the latter two are optional independent scenarios. In the first two scenarios, students must compare three different shock absorbers (or shocks) for the trailer....