1 / 16

Modeling with Differential Equations

Modeling with Differential Equations. Dr. Jeff Morgan Department of Mathematics University of Houston jmorgan@math.uh.edu. Shameless Advertisement. Houston Area Calculus Teachers Association – http://www.HoustonACT.org Houston Area Teachers of Statistics – http://www.HoustonATS.org

yetta-benjamin
Download Presentation

Modeling with Differential Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Modeling with Differential Equations Dr. Jeff Morgan Department of Mathematics University of Houston jmorgan@math.uh.edu

  2. Shameless Advertisement • Houston Area Calculus Teachers Association – http://www.HoustonACT.org • Houston Area Teachers of Statistics – http://www.HoustonATS.org • Online practice AP Calculus and Statistics Exams – April and May 2009. See the links above. • UH High School Mathematics Contest – http://mathcontest.uh.edu • teachHOUSTON – http://teachHOUSTON.uh.edu • Online Masters in Mathematics - http://www.math.uh.edu/Matweb/grad_mam.htm

  3. Goals • Create a mathematical model for the motion of a cart along an arbitrary roller coaster track lying in the xy plane, subject to gravity in the -y direction. • Examine the specific case of a circular track, and build an animation of the motion. • Consider the added complexity of a spring loaded roller coaster model, and modify the mathematical model. • Determine whether there is a spring loaded model on which the speed of the cart would always be constant. • Modify the spring model to incorporate a bungee cord.

  4. A Review of Projection and Component u u v v

  5. Roller Coaster Models(neglecting friction) track gravity cart

  6. Creating the Mathematical Model

  7. Specific Example: Circular Track(neglecting friction) track gravity cart

  8. Process • Write Model Equations. • Solve using Winplot. • Export data to Excel. • Fit Data. • Animate the motion in Winplot.

  9. Spring-Loaded Roller Coaster Models(neglecting friction) spring secure end track gravity cart

  10. Creating the Mathematical Model

  11. track gravity cart Specific Example: Spring-Loaded Circular Track(neglecting friction) secure end

  12. Process • Write Model Equations. • Explore using Winplot. • Discuss animating the motion.

  13. Exploration: Determine whether there a spring-loaded roller track so that the speed of the cart along the track is always constant.

  14. Exploration: How will the model change if we use a bungee cord instead of a spring?

  15. An Important Example:

  16. Exploration: Determine whether there a bungee coaster roller track so that the speed of the cart along the track is always constant.

More Related