Tags: second order

All Categories (1-20 of 40)

  1. 2021-Radhka, T. S. L. - Notes on Frobenius method

    06 Sep 2021 | Contributor(s):: T S L Radhika

    Radhka, T. S. L. 2021. Notes on Frobenius methodAbstract: This article explains and demonstrates applications of the Frobenius theory as discussed in thebook by Simmons on “Differential Equations with Applications and Historical Notes.” We specificallydiscuss the...

  2. 3-073-S-EarthQuake Part II

    06 Aug 2021 | | Contributor(s):: Tracy Weyand

    This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring-damper system. In this activity, students will analyze motion of the roof under different damping and vibration...

  3. 3-072-S-EarthQuake Part I

    06 Aug 2021 | | Contributor(s):: Tracy Weyand

    This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring system. In this activity, students will analyze the motion of the roof caused by ground movement. Here we...

  4. 3-092-S-WirelessPower

    04 Aug 2021 | | Contributor(s):: Maila Hallare, Iordanka Panayotova

    This activity presents an engineering application that is modelled by a coupled system of two linear second-order differential equations with constant coefficients. One of the equations is homogeneous while the other one is non-homogeneous. The application is called wireless power transmission...

  5. 3-099-S-PullBack

    03 Aug 2021 | | Contributor(s):: Brody Dylan Johnson

    This hands-on modeling scenario guides students through the development of an empirical model for the velocity and distance traveled of a simple pull-back toy. Students can record videos and extract data using their own pull-back toy or use data included in the student version. Two different...

  6. 3-076-S-CircuitBuilding

    27 Jul 2021 | | Contributor(s):: Chiu Choi

    In this project students will establish a mathematical model for an electric circuit as a second-order ordinary differential equation with constant coefficients. They will derive the initial conditions for this differential equation by using circuit laws. They will obtain its closed-form solution...

  7. 3-105-S-FrequencyResponse

    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.

  8. 3-034-S-CarSuspensions

    14 Jul 2020 | | Contributor(s):: Therese Shelton, Brian Winkel

    We examine the spring-mass-dashpot 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.

  9. 3-027-S-BobbingDropping

    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.

  10. 2020-Winkel, Brian - Remote Teaching Module - Spring Design to Meet Specs at Minimum Costs

    16 Jun 2020 | | Contributor(s):: Brian Winkel

    We place here all the materials in support of the SIMIODE Remote Teaching Module - Spring Design to Meet Specs at Minimum Costs. This  Module is about second order, linear, ordinary differential equations.The class lesson starts with building a model of a spring-mass using...

  11. 3-026-S-SpringInverseProblem

    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.

  12. 3-031-S-SpringCost

    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.

  13. 2016-Keszei, Ernő - Chemical Kinetics for Beginners. 

    27 Mar 2020 | | Contributor(s):: Brian Winkel

    Keszei, Ernő. 2016.  Chemical Kinetics for Beginners. Course material supported by the Higher Education Restructuring Fund allocated to ELTE by the Hungarian Government.Table of ContentsContents 31. Introduction 42. Formal kinetic description of elementary reactions...

  14. 2013-Sutton-SecondOrderLinearODE's-PartII

    27 Mar 2020 | | Contributor(s):: Brian Winkel

    2013-Sutton-SecondOrderLinearODE's-PartIIPresentation 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

  15. 2018-Chen, Franklin M. - Teaching Kinetics through Differential Equations Constructed with a Berkeley MadonnaTM Flow Chart Model.

    26 Mar 2020 | | Contributor(s):: Brian Winkel

    Chen, Franklin M. 2018.  Teaching Kinetics through Differential Equations Constructed with a Berkeley MadonnaTM Flow Chart Model. Journal of Computational Science Education. 9(1):...

  16. 2011-CasaXPS-Mechanics Applications DEs

    20 Mar 2020 | | Contributor(s):: Brian Winkel

    2011-CasaXPS-Mechanics Applications DEsCasaXPS. 2011 Variable Forces and Differential Equations. www.casaxps.com. See https://www.simiode.org/resources/7150/download/2011-CasaXPS-Mechanics_ApplicationsDEs.pdf .    Table of ContentsVariable Forces...

  17. 2012-Ehrke, 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.

  18. 2008-San Andrés, Luis - Dynamic Response of Second Order Mechanical Systems with Viscous Response Forces

    16 Mar 2020 | | Contributor(s):: Brian Winkel

    San Andrés, Luis. 2008. Dynamic Response of Second Order Mechanical Systems with Viscous Response Forces.  MEEN 617 Notes-Presentation. 39 pp.See https://oaktrust.library.tamu.edu/handle/1969.1/93269 .Walk through the cases in context of second order linear constant...

  19. 3-150-S-ItsABlastFurnace

    13 Aug 2019 | | Contributor(s):: Kurt Bryan

    This project uses the steady-state 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 steady-state, so that only an elementary ordinary differential equation (ODE) is needed, and...

  20. 3-130-S-MatterOfSomeGravity

    07 Aug 2019 | | Contributor(s):: Kurt Bryan

    This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation. The theme of the project is that one often has a physical model for a system but in which the model contains unknown parameters or...