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ase311_hw7 - ASE 311 Engineering computation Fall 2009...

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ASE 311 Engineering computation, Fall 2009, Homework 7 Due: Friday, October 23, 2:00 PM in the lecture room JGB 2.216 Report all work, including any m -files you have written. You may also find the command diary useful in recording your MATLAB session. Please write clearly and be sure to label for which problem each solution is. Please, staple Part I and Part II separately and make sure that your name is written on both parts. Part I 1. [Newton-Raphson] Determine a solution for the nonlinear equations u1D453 1 ( u1D465 1 , u1D465 2 ) = u1D465 2 1 + u1D465 2 2 5 = 0 u1D453 2 ( u1D465 1 , u1D465 2 ) = u1D465 2 1 u1D465 2 1 = 0 using MATLAB and the Newton-Raphson method with initial guesses of u1D465 1 = u1D465 2 = 1. How many iterations do you need in order to have ∣∣ u1D453 ( u1D465 ) ∣∣ 2 < 10 4 ? 2. [Mass-spring system] Using the same approach as in the lectures or section A.2 of the book, derive the following set of equations for a system with three masses and four springs between two fixed walls: 2 u1D458 u1D45A 1 u1D458
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