ME17PS2 2008

# ME17PS2 2008 - ME17 Summer, 2008 Problem Set #2 Due Tuesday...

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ME17 Summer, 2008 Problem Set #2 Due Tuesday July 8th at class time Reading: Chap. 3, Section 3.1.2: Chap. 6, Sections 6.1-6.3: Chap. 8, all; Chap. 9, Sections 9.1-9.3; Chap 10, Sections 10.1, 10.2,; Handout on Matrix Algebra. Announcement: Midterm will be on Thursday, July 10th. Comment: This problem set is about root-finding methods, couched around the “bungee” problem, and the “ballistics” problem. It is not particularly easy. Start the problems early. Problem 1. (The bungee problem) Solve the bungee problem, i.e find the mass that makes v=36m/s at t=4s for Earth gravity and C D = 0.25 kg/m, using the Bisection and False Position methods. Use a convergence criterion of at least 5 significant figures for the mass, m and satisfy the equation, i.e. have f(m) = 0 to within an absolute error of 10 - 3 . In both cases, use starting guesses of m = 50 kg and 200 kg. (i) Take the M-file for Bisection that Guarav has posted and run it for the parameters given above. Then modify it to store the successive estimates of m in a vector and plot the value of m vs. the iteration number. Compare your results with those in the Table in Section 5.4. (ii) Modify the M-file for Bisection to turn it into one that uses the Method of False Position. (Save this as a new M-file for use in later problems.) This will involve your changing the logic by which the two points for the next iteration are chosen. Solve the bungee problem using the false position method and plot the value of m vs. the iteration number, as above. Which method takes fewer iterations? The results of this problem should be two M-files and two plots, plus a short discussion.

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## ME17PS2 2008 - ME17 Summer, 2008 Problem Set #2 Due Tuesday...

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