ASE311 HW1 pdf

ASE311 HW1 pdf - has ceased Part II 3[Chapra Problem 4.3...

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ASE 311 Engineering computation, Fall 2009, Homework 1 Due: Friday, September 4, 2:00 PM in the lecture room JGB 2.216 Report all work, including any m -fles you have written. You may also fnd the command diary use±ul in recording your MATLAB session. Please write clearly and be sure to label ±or 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. [Chapra, Problem 1.1] Use calculus to veri±y that v ( t ) = r gm c D tanh pr gc D m t P (1) where tanh x = ( e x - e - x ) / ( e x + e - x ), is the solution o± dv dt = g - c D m v 2 (2) 2. [Euler’s method ±or (2)] Let m = 85 kg, g = 9 . 81 m / s 2 and c D = 0 . 33 kg / m. Using MATLAB , compute v ( t i +1 ) = v ( t i ) + ± g - c D m v ( t i ) 2 ² ( t i +1 - t i ) ±or t i = 0 , 2 , 4 , . . . 16 s starting ±rom v (0) = 0 m / s. Plot the result and the exact solution (1) in the same fgure. What is the terminal velocity, i.e. the velocity attained when acceleration
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Unformatted text preview: has ceased? Part II 3. [Chapra, Problem 4.3] Determine the smallest number in MATLAB that when added to one gives a number greater than one. Compare with the built-in ±unction eps . Hint: Do not use the variable name eps yoursel±. 4. Compute manually the limits L 1 = lim x → sin x x and L 2 = lim x → 1-cos x x 2 You may rely on the Maclaurin series ±or sin , cos: sin x = x-x 3 3! + x 5 5!- · · · and cos x = 1-x 2 2! + x 4 4!- · · · 5. Compute L 1 and L 2 using MATLAB by evaluating the expressions sin x/x and (1-cos x ) /x 2 at x = 10-i , i = 2 , 4 , 6 , 8 , 10. Do you observe something strange?...
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