q2sols18085f05

q2sols18085f05 - MIT OpenCourseWare http:/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu 18.085 Computational Science and Engineering I Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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18.085 Quiz 2 November 14, 2005 Professor Strang Your PRINTED name is: Grading 1 2 3 1) (34 pts.) A point load at rc = i hangs at the same point where c(rc) changes fro111 c = 1 (for 0 < rc < i) to c = 2 (for i < rc < 1). Both ends are FIXED. (a) Solve for u(rc) and w(rc) = c(rc) ul(rc): (b) Draw the graphs of u(rc) and w(rc) (c) Divide the hanging bar into irltervals of lerlgtl~ h = (then c(rc) changes fro111 1 to 2 at rc = 2h). There are unknowrls U = (ul, . . . ,US)at the rneshpoints. Write down a rrlatrix approximation KU = F to the equation above. Take differences of differences (each difference over an interval of length h).
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Solution Then c(rc) ul(rc) = w(rc) gives (includirlg c(rc) = 1 or 2) (c) Finite difference approximation KU = F w = c(rc) dwldrc is approximated by U1-0 U2-Ul h h ' -- U3-U2 2- h ' Uq-U3 2- h ' Us-Uq 2- h 0-US 2- ' h Then dwldrc is approximated by
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q2sols18085f05 - MIT OpenCourseWare http:/ocw.mit.edu...

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