M2250-2 Second Lab Assignment

MATH 2250 § 2	SECOND LAB ASSIGNMENT	Oct. 22, 2002
A. Treibergs		Due Nov. 8, 2002

Read the description of the second lab assignment. Here you will find a film clip of the collapse of the Tacoma Narrows Bridge. You will also find two models that attempt to describe the motion of the bridge. Although our lab shall be concerned with the simpler forced oscillation models of the spring-mass and spring-dashpot-mass systems, at least you will get a feel for how these models can be extended into more realistic models of an oscillating bridge.
http://www.math.utah.edu/~korevaar/2250fall02/tnarrows/
http://www.math.utah.edu/~gustafso/tnarrows/index.html
More discussion of the undamped free oscillation equation, the forced undamped oscillation equation which exhibits resonance and blowup, the damped forced oscillation equation and its frequency response curve is available in my tutorial.
http://www.math.utah.edu/~treiberg/M2280L3.mws
Do all parts of problems 2.1-2.4. Remember, that this is a lab writeup whose purpose is to show how the computer plays a role in solving problems. It is not just an exercise in running somebody's code. Please make your writeups SELF-CONTAINED. This simply means that for each problem you would include a sentence or two stating what the problem is about, how it differs from the other problems and your conclusions. Explain any intermediate computation. For example, before you make the computation that shows that your system is overdamped, you would say that you are checking for overdampedness and state what the condition is. You can use the templates, provided that they're suitably enhanced. It is perfectly OK to write by hand on your output. Or use MAPLE's capability of inserting comment text.
Each of the problems will be worth 20 points. If you wish, but this is strictly optional, you may do problems 2.5 and 2.6. These will be worth 10 extra credit points apiece.