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A4 - Applied Math 250 Assignment#4 Spring 2009 Not for...

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Unformatted text preview: Applied Math 250 Assignment #4 Spring 2009 Not for submission Treat this assignment as practice for Term Test #1 and the ﬁnal exam. Solutions will be posted, but examples of applications such as these are not easy to come up with, so I strongly encourage you to try each problem honestly before checking the solutions. If you’re having trouble, read the solution to one problem, then try the rest of the problems again; if you just read through the solutions you won’t have any more problems to practise on! A/ Problem Set 2 #6, #7, #9, #10, #11, #12, #13 B/ Problem Set 1 #15, with the following modiﬁcations: a/ i) Consider PSl #15a. What can you predict about t, from Buckingham’s Theorem? ii) Find t, explicitly. b/ i) Now consider PSl #15b. What can Buckingham’s Theorem tell us in this case? Note: since we’re hoping to isolate t, try choosing dimensionless vari— ables such that t appears in only one of them. ii) Try to find t,. It is in fact not possible to do this exactly, since the last step requires solving an equation of the form e” + bu: = 0. Approximate the solution, by using a second order Maclaurin polynomial as an approximation for the exponential term and solving the resulting quadratic for tr. Under What conditions is this approximation justiﬁable? Note: In both a) and b), you can solve for v(t), and then integrate to ﬁnd the height h(t) before setting h = O. ...
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