
3073SEarthQuake Part II
06 Aug 2021   Contributor(s):: Tracy Weyand
This modeling scenario considers a onestory building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a massspringdamper system. In this activity, students will analyze motion of the roof under different damping and vibration...

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....

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,...

2018Gavin, Henri P. 2018. Dynamics of Simple Oscillators (single degree of freedom systems)
24 Mar 2020   Contributor(s):: Brian Winkel
Gavin, Henri P. 2018. Dynamics of Simple Oscillators (single degree of freedom systems). Department of Civil and Environmental EngineeringDuke University. Notes. 39 pp.IntroductionThis document describes free and forced dynamic responses of simple oscillators (sometimes...

2012Ehrke, John. 2012. Second Order Equations, Three Cases. Presentation.
20 Mar 2020   Contributor(s):: Brian Winkel
Ehrke, 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.

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...

2009Shamim, Sohaib, Wasif Zia, and Muhammad Sabieh Anwar  Investigating viscous damping using a webcam
16 Mar 2020   Contributor(s):: Brian Winkel
Shamim, Sohaib, Wasif Zia, and Muhammad Sabieh Anwar. 2009. Investigating viscous damping using a webcam. 12 pp.See https://aapt.scitation.org/doi/10.1119/1.3298370 .Abstract: We describe an experiment involving a mass oscillating in a viscous fluid and analyze overdamped,...

2012Sharma, P. K.  Transient State Analysis of a damped & forced oscillator.
13 Mar 2020   Contributor(s):: Brian Winkel
Sharma, P. K. 2012. Transient State Analysis of a damped & forced oscillator. International Journal of Computers Electrical and Advanced Communications Engineering. 1(2):190196.Abstract: This paper deals with the behaviour of an oscillator in its initial stage of oscillation. How...

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...

2008WittHansen, Ole  Examples Of Differential Equations In Physics.
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...

2017Morin, David  Oscillations  Notes
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...

2009May, James E.  Nonlinear vibration control of long flexible structures employing intermodal energy transfer (modal damping). PhD Thesis.
09 Sep 2017   Contributor(s):: Brian Winkel
May, James E. 2009. Nonlinear vibration control of long flexible structures employing intermodal energy transfer (modal damping). PhD Thesis. University of Akron. 314 pp.From the introductionIn the not too distant past, the design philosophy for tall civil structures could be...

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.

2017Winkel, Brian  Stay Tuned  Modeling in Differential Equations Courses
29 Dec 2016   Contributor(s):: Brian Winkel
Joint Mathematics Meetings 2017 Teaching and Learning of Undergraduate Ordinary Differential Equations, I 10:20 AM Friday, 6 January 2017Marriott Marquis, A702 Atrium Level Stay Tuned Modeling in Differential Equations...

3030SSecondOrderIntro
22 Apr 2016   Contributor(s):: Brian Winkel
SPANISH LANGUAGE VERSION We have placed in Supporting Docs both Student and Teacher Version (LaTeX and PDF Versions) with a Spanish LaTeX Class file, SIMIODESPANISH.cls. Names will be xySTitleStudentVersionSpanish and xyTTitleTeacherVersionSpanish.

1999Marchand, R. and T. J. McDevitt  Learning Differential Equations by Exploring Earthquake Induced Structural Vibrations: A Case Study
20 Jun 2015   Contributor(s):: T. J. McDevitt, Richard Marchand
Marchand, R. and T. J. McDevitt. 1999. Learning Differential Equations by Exploring Earthquake Induced Structural Vibrations: A Case Study. International Journal of Engineering Education. 15(6): 477485.See https://www.ijee.ie/articles/Vol156/ijee1107.pdf .Article...

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...