## Tags: second order

### All Categories (1-20 of 43)

1. 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 inverse-square of the distance between the centers of mass of the Earth and the projectile. When projectiles are near to Earth's surface,...

2. 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...

3. 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 spring-mass systems and solved second-order...

4. 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...

5. 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...

6. 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...

7. 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...

8. 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...

9. 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...

10. 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.

11. 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.

12. 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.

13. 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...

14. 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.

15. 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.

16. 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...

17. 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

18. 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):...

19. 20 Mar 2020 | | Contributor(s):: Brian Winkel