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ME218 Homework 1

# ME218 Homework 1 - Hint To find c we need to solve equation...

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ME 218 - ENGINEERING COMPUTATIONAL METHODS Homework # 1 Assigned: September 1 st , 2011 Due: September 8 th , 2011 Name: _____________________ UT EID: _______ Section Unique Number: _________________ Problem 1: Velocity of a mass m in linear viscous drag with the coefficient of viscosity c (hence, drag force is Fd=-cv, where v is velocity of the mass) is described by the equation (you’ll learn in ME344 how to derive this): ࠵? ࠵? = ࠵?࠵? ࠵? ( 1 ࠵? ! ! ! ! ) Let’s pretend this is a free-fall parachuter of mass m=68.1kg and we wish to know what the viscosity of air (coefficient c) is if after 10 seconds the velocity of the parachute is measured to be 40 m/s (he/she better open that chute or else ). Let us use g=9.8 N/kg and the bisection method as the solution method, if we know that c is between 12 and 16 N/(m/s). Please locate c to within 0.5 N/(m/s) and tabulate your results nicely to show all iterations.

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Unformatted text preview: Hint: To find c, we need to solve equation that will result in the following 40 = 9 . 8 ∙ 68 . 1 ࠵ ( 1 − ࠵ ! ! !" . ! !" ) or in other words, we need to solve ࠵ ࠵ = 9 . 8 ∙ 68 . 1 ࠵ 1 − ࠵ ! ! !" . ! !" − 40 = Problem 2 For the function ࠵ ࠵ = 3 ࠵ + sin ࠵ − ࠵ ! , find one root in the interval [0,1] (i.e. ࠵ ! = , ࠵ ! = 1 using the bisection method. Terminate your calculations when you are certain that the error between your approximation and actual solution to the equation ࠵ ࠵ = is less that 0.05. Explain why and how you decided to stop further iterations of bisecting the interval. Problem 3 Comment on the pro-s and con-s of the bisection and false position methods (the false position method was discussed at the end of the lecture on September 1 st , 2011)....
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ME218 Homework 1 - Hint To find c we need to solve equation...

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