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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 6.16.3:
Chap. 8, all;
Chap. 9, Sections 9.19.3;
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 rootfinding 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 Mfile 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 Mfile for Bisection to turn it into one that uses the Method of False Position.
(Save this as a new Mfile 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 Mfiles and two plots, plus a short discussion.
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 Summer '07
 Milstein

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