Math 333 Lab Projects

  1. Lab 1 is due at 5:00 pm on Thursday, February 21. You should work in groups of no more than three. By 5:00 pm on Tuesday, February 12, one representative from each group must send me an email to tell me the names of all of the group members. The assignment is as follows:

    Complete Lab 2.4 (A Mass-Spring System with a Rubber Band) on p. 229-231 of your textbook. This lab will be important in our analysis of second-order differential equations, as well as in our analysis of the Tacoma Narrows bridge. Each group should submit a typed report in which you address each of parts 1-4 of the lab in order. Feel free to include graphs and/or figures to supplement your discussion of the questions, but make sure that you explain clearly (in words) any graphs or figures that you include in your report. Note that you can export graphs in Maple as image files by right-clicking on the graph that you want to export. You can type the report in Microsoft Word, Open Office (open-source office software), Maple, Latex, Tex, or any other type-setting program that you prefer.

    To complete parts 3 and 4 of Lab 2.4, you will need to include a piece-wise defined function in your system of differential equations. This Maple file illustrates the syntax for generating piece-wise defined functions. This Maple worksheet is posted on the P: drive at P:/Class/Math/Paquin/DiffEq/Piecewise.mw.

    Finally, feel free to experiment with actual masses, springs, and rubber bands!

  2. Lab 2 is due at 5:00 pm on Friday, April 18. In this lab, you will investigate differential equations models for the motion observed on the Tacoma Narrows Bridge on November 7, 1940. Your primary reference for this lab is Section 4.5 in your textbook; see the posted assignment for more details. You may also wish to use the research article Large-amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Non-linear Analysis by A.C. Lazer and P.J. McKenna, in SIAM Review, Vol. 32, No. 4, 1990, pp. 537-578. There are, of course, numerous other references on the web and elsewhere on the dynamics of suspension bridges in general and the Tacoma Narrows Bridge in particular, and you are welcome to use any references that you choose. Make sure that you properly cite any references that you use.