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q2_sol_18085_f06

q2_sol_18085_f06 - 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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4 5 18.085 Quiz 2 November 3, 2006 Professor Strang Your PRINTED name is: SOLUTIONS Grading 1 2 3 4 1) (25 pts.) This network (square grid) has 12 edges and 9 nodes. 1 2 3 3 / 4 u 2 = 1 3 / 4 1 / 2 6 1 / 2 1 / 2 1 / 4 7 8 9 1 / 4 u 8 = 0 (a) Do not write the incidence matrix ! Do not give me a MATLAB code ! Just tell me: (1) How many independent columns in A ? 8 (2) How many independent solutions to A T y = 0 ? 12 8 = 4 (3) What is row 5 (coming from node 5) of A T A ? I do want the whole of row 5. 0 1 0 1 4 1 0 1 0 (b) Suppose the node 2 has voltage u 2 = 1, and node 8 has voltage u 8 = 0 (ground). All edges have the same conductance c . On the second picture write all of the other voltages u 1 to u 9 . Check equation 5 of A T Au = 0 (at the middle node). 1 1 1 + 4 1 0 = 0 2 2 2 1
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2) (25 pts.) Suppose that square grid becomes a plane truss (usual pin joints at the 9 H V H V nodes). Nodes 2 and 8 now have supports so u 2 = u 2 = u
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