q118085f03sol

# q118085f03sol - MIT OpenCourseWare http:/ocw.mit.edu 18.085...

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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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Solutions 18.085 Quiz 1 Professor Strarlg October 6, 2003 1) (30 pts.) A systcrn with 2 springs and masses is fixed-free. Constants arc ell c2. VyLLuo=O (a) Write dom.11 the rnatriccs A arid K = ATCA (b) Prove by two tests (pivots, dctcrrninants, indcpcridcncc of colurnns of A) that this matrix K is (positivc definite) (positivc scrnidcfinitc). Tell me which two tests you are using! Dctcrrninarits of h': cl + c2 (1 x 1) and clc~ ((2 x 2) Pivots of c1 + c2 arid clca/(cl + c2) Indcpcridcncc of colurnns of A: (1, -1) and (0,l) All prove positivc definiteness of K (c) hlultiply column times row to corriputc the "clcrncnt rnatriccs" KI, h;: Cornputc Kl = (column 1of rlT)(c~)(row 1 of A) 7 1 - 11 01 - "Lo 01 Cornputc h; = 2 of rlT)(c2)(row 2 of A) r -11 Then h' = KI + K2. What vectors solve K2 For those displaccmcrlts JI and x2, what is the energy in spring 2?
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## This note was uploaded on 04/12/2011 for the course MATH 18.085 taught by Professor Staff during the Fall '10 term at MIT.

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q118085f03sol - MIT OpenCourseWare http:/ocw.mit.edu 18.085...

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