ME218_HW5_Fall2010 - m falling with initial velocity zero...

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ME 218: ENGINEERING COMPUTATIONAL METHODS Home Work #5 Assigned: October 16, 2010 Due: October 21, 2010 Name: __________________UT EID: ____________Unique: _________ Lab Time: (Mon/Tue) ___PM Problem 1: Vectorial Newton-Raphson Method (similar to the lecture example, just some numbers are changed) Find an intersections of curves ݔ ൅ݕ ൌ9 (a circle) ݁ ݕൌ1 (an exponential curve) that is close to the point ሺ3.0, െ3.0ሻ . Use the vectorial Newton Raphson method starting from the point ሺݔ ሻ ൌ ሺ3.0, െ3.0ሻ and perform 3 iterations of the method. Feel free to use any software or programming tool at your disposal. If you do, please enclose information about how you used the software tool and/or the relevant program listings. Problem 2: Vectorial Newton-Raphson Method (more interesting problem – good for practice) Velocity of a paraglider of mass
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Unformatted text preview: m falling with initial velocity zero through the air (gaseous fluid) with the coefficient of linear friction c is described as a function of time by the following equation (you will learn this in ME344): v ( t ) = mg c 1 − e − ct m ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Let us assume we know that the gravitational constant g =9.81 N/kg. In order to estimate the mass of the paraglider m and the coefficient of viscous friction c , we snap measurements of velocity at time t=5s and t=10s. We obtain that v (5) = 29.9 m/s, and v (10) = 40 m/s. Start with the initial guess of m = 70 kg and c = 0.1 N/(m/s). Perform 5 iterations of the multivariate Newton Raphson method and please show your steps for full credit. Please feel free to use any software and/or programming tool at your disposal (if you do, please enclose a description how you did it or the listing of your program)....
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