ME218_HW5_Fall2011(2) - v ( t ) = mg c 1 e ct m # $ %...

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ME 218: ENGINEERING COMPUTATIONAL METHODS Home Work #5 Assigned: October 6, 2011 Due: October 13, 2011 Name: __________________UT EID: ____________Unique: _________ Lab Time: (Mon/Tue) ___PM Problem 1: Find an intersections of curves ! ! + ! ! = 9 (a circle) ! ! ! = 2 (an exponential curve) that is close to the point ( 0 , 1 ) . Use the vectorial Newton Raphson method starting from the point ! ! , ! ! = ( 0 , 1 ) and perform 3 iterations of the method and do it using a simple scientific calculator (use a computer to perhaps confirm your findings). Please maintain 4 decimal digits throughout your calculations. Problem 2: (basically, a variation of the example postulated in class) Velocity of a mass 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):
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Unformatted text preview: 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 m that is falling through the air and the coefficient of viscous friction c , we snap measurements of velocity at time t=5s and t=10s. We obtain that v (5) = 31.1 m/s, and v (10) = 40 m/s. Start with the initial guess of m = 30 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 the listing of your program). Please enclose your results neatly tabulated so that we can run through your results with ease. Also, please report just 4 decimal digits in your work thanks!...
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