
4036SAltitudeDependentGravity
22 Jan 2022   Contributor(s):: Jakob Kotas
Basic projectile motion without air resistance typically assumes gravity is constant. In reality, the acceleration due to gravity is proportional to the inversesquare of the distance between the centers of mass of the Earth and the projectile. When projectiles are near to Earth's surface,...

4039SFallingDarts
21 Jan 2022   Contributor(s):: Jacob Paul Duncan
Most projectile motion and free fall models are based on the assumption that gravity is the only force acting on the object. Here we develop, solve, and analyze a second order nonhomogeneous differential equation model for free fall which incorporates air resistance. Students will solve the model...

3091SMassSpringExperiments
14 Jan 2022   Contributor(s):: Bonnie Moon
In this lab students will collect data on their spring mass systems and compare their empirical models to their theoretical ones—giving them an opportunity to actually test a model against data. Before this lab, students should have modeled springmass systems and solved secondorder...

2021Radhka, 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...

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...

3072SEarthQuake Part I
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 massspring system. In this activity, students will analyze the motion of the roof caused by ground movement. Here we...

3092SWirelessPower
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 secondorder differential equations with constant coefficients. One of the equations is homogeneous while the other one is nonhomogeneous. The application is called wireless power transmission...

3099SPullBack
03 Aug 2021   Contributor(s):: Brody Dylan Johnson
This handson modeling scenario guides students through the development of an empirical model for the velocity and distance traveled of a simple pullback toy. Students can record videos and extract data using their own pullback toy or use data included in the student version. Two different...

3076SCircuitBuilding
27 Jul 2021   Contributor(s):: Chiu Choi
In this project students will establish a mathematical model for an electric circuit as a secondorder ordinary differential equation with constant coefficients. They will derive the initial conditions for this differential equation by using circuit laws. They will obtain its closedform solution...

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.

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.

2020Winkel, 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 springmass using...

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.

2016Keszei, 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...

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

2018Chen, 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):...

2011CasaXPSMechanics Applications DEs
20 Mar 2020   Contributor(s):: Brian Winkel
2011CasaXPSMechanics Applications DEsCasaXPS. 2011 Variable Forces and Differential Equations. www.casaxps.com. See https://www.simiode.org/resources/7150/download/2011CasaXPSMechanics_ApplicationsDEs.pdf . Table of ContentsVariable Forces...

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.