HW5 Solution

# HW5 Solution - ME 218 ENGINEERING COMPUTATIONAL METHODS...

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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): v ( t ) = mg c 1 e ct m # \$ % ' ( Let us assume we know that the gravitational constant

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HW5 Solution - ME 218 ENGINEERING COMPUTATIONAL METHODS...

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