Due: Your report must be submitted by 10 a.m. on Friday, April 16.

Group project: This is a group project with each group having either three or four members. Once a group begins work on the project, its membership cannot change. Consequently establishing your group must be your first step in this project. Each group will submit one report, and all members of the group will receive the same grade for this project.

Goals:

1. To become familiar with the long-term behavior of solutions to certain forced second-order equations.
2. To study the relationship between the frequency of the forcing and the amplitude of the solutions.

Second-order equations: Using all of the methods that we have developed in this course, you will analyze the long-term behavior of the solutions to two similar forced, second-order equations. Follow this project description.

Your report: Your report should be no longer than five typewritten pages, and it should address all of the questions mentioned above. You may provide as many illustrations as you wish, but the relevance of each illustration to your report must be evident. (Please remember that, although one good illustration may be worth 1000 words, 1000 illustrations are worth nothing.) Illustrations are part of the five-page limit. Please insert your illustrations at appropriate places in your report rather than attaching them to the end of the report.

Numerical simulation: For part 4 of the project, you may want to use a program called CantileverPMap in conjunction with HPGSystemSolver. I have implemented an on-line version of the program using the Math Department's webMathematica site. It works fine, but only two users run it at the same time. My guess is that this will not be a problem until Tuesday night.

Parameter values: The value of k that you should use is determined by the last digits of the BU ID numbers of the members of your group. Use k = 0.05 a + 0.4 where a is the average of the last digits of all members in the group. Round k to two decimal places of accuracy. For example, if the last digits are 0, 1, 2, and 2, then a = 1.25 and k = 0.46.

Asking questions: Questions by email about the project are not allowed. Instead we will once again use the Blackboard Discussion Board for this course. I will check that board for questions at least once a day. The last time that I will check the discussion board will be noon on April 15. Do not wait until the last minute to ask questions. Please start a new thread with each new question.

Academic Conduct: Your work and conduct in this course are governed by the CAS Academic Conduct Code. This code is designed to promote high standards of academic honesty and integrity as well as fairness. A copy of the code is available in CAS Room 105 if you cannot access it on the web, and it is your responsibility to know and follow the provisions of the code. In particular, all work that you submit in this course must be your original work. For example, you can only discuss your project with other members of your group, with Blanchard, or with Veillette. Moreover, the computations that you do for your report as well as the text of your report must be original to your group. All group members are responsible for all aspects of the report. Any cases of suspected academic misconduct will be reported to the CAS Dean's Office.