11 Pages

# Exam 2 Solution

Course Number: MEEN 357, Fall 2009

College/University: Texas A&M

Word Count: 2253

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Spring 2009 EXAM 2 MEEN 357 March 26, 2009 Dr. Bowen Name: ____________________________________________ "Aggies do not lie, cheat, or steal, nor do they tolerate those who do." Aggie Code of Honor By my signature below I pledge that my conduct on this exam is consistent in every way with the Aggie Code of Honor: Signature: ____________________________________________ 1. This exam consists of six (6)...

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Texas A&M - MEEN - 357
Lecture 1MEEN 357 Homework Solution1Solve the Following Problems in the Command Window 1. What command would you enter into the Command Window in order to evaluate the quantity? What is the value you calculated?( 3.4 + 7 )Solution: Type and execute3
Texas A&M - MEEN - 357
Lecture 2MEEN 357 Homework Solution11. Problem 3.1 of the textbook. There is not a unique m-file. The following one has the essential elements. It also has comments inserted that might assist in understanding the approach. Solution:%Problem 3.1 on pag
Texas A&M - MEEN - 357
Lecture 3MEEN 357 Homework Solution11. Convert the following 64 bit number to a real number:S =1 Exp = 10010001111 M = 1100001101010000000010000000000000000000000000000000Solution: There are a lot of different ways to do the arithmetic, including by
Texas A&M - MEEN - 357
Lecture 5MEEN 357 Homework Solution11. Problem 4.19 of the textbook. Solution: You are given a functionf ( x ) = x3 2 x + 4(5.1)and asked to find a) forward first derivative, b) backward first derivative, c) centered first derivative, d) forward sec
Texas A&M - MEEN - 357
Lecture 6MEEN 357 Homework Solution11. Problem 6.15 of the textbook. You are to use the false position method. Solution: You are given the function r h 2 V = r 2 cos 1 ( r h ) 2rh h L r (6.1)and asked to find the h when V = 8.5 , r = 2 and L = 5 . In
Texas A&M - MEEN - 357
Lecture 7MEEN 357 Partial Homework Solution11. Problem 6.12 of the textbook. You are to use the Newton Raphson method to find the real root of the polynomialf ( x ) = 0.0074 x 4 0.284 x 3 + 3.355 x 2 12.183 x + 5(7.1)in the interval [15, 20] . You a
Texas A&M - MEEN - 357
Lecture 8MEEN 357 Homework Solution11. Modify the script on page 11 above so that it will implement the Gauss-Jordan method for the same problem, i.e., for the same A and b . Solution: The script on page 11 is%Primitive Gaussian Elimination for n=3. c
Texas A&M - MEEN - 357
Lecture 10MEEN 357 Homework Solution11. Problem 12.1(a) of the textbook. Solution: You are asked to use the Gauss-Seidel method to solve0 x1 41 0.8 0.4 0.4 0.8 0.4 x = 25 2 0.4 0.8 x3 105 0 (10.1)You are instructed to continue the iteration until th
Texas A&M - MEEN - 357
Lecture 11MEEN 357 Homework Solution11. Problem 13.5 of the textbook. Solution: This problem is almost identical to the Example on page 16 of the notes for Lecture 11. Given the table of data in the problem statement, the following script produces the
Texas A&M - MEEN - 357
Lecture 12MEEN 357 Homework Solution11. Problem 13.31 of the textbook. Solution: The approach you must follow is to use the kind of argument given in Lectures 11 and 12. You are given an equation = De B /TThe linear version of this nonlinear equation
Texas A&M - MEEN - 357
Lecture 13MEEN 357 Homework Solution11. Problem 14.8 of the textbook. Solution: You are asked to apply multiple liner regression to the data x1 x2 y 0 0 15.1 1 1 17.9 1 2 12.7 2 1 25.6 2 2 20.5 3 1 35.1 3 2 29.7 4 1 45.4 4 2 40.2This problem is virtua
Texas A&M - MEEN - 357
Lecture 14MEEN 357 Homework Solution11. Problem 15.5 of the textbook. Solution: You are given the datax f ( x)1 02 52.5 73 6.54 25 0Part a): You are asked to use Newtons interpolation polynomial determine the interpolated value at x = 3.4 for t
Texas A&M - MEEN - 357
Lecture 15MEEN 357 Homework Solution11. Problem 17.2 of the textbook. This problem should be turned in, as usual, at the start of class. Solution: You are to evaluate the integralI = (1 e 2 x ) dx4 0(15.1)a) b) c) d) e) f)Analytically Single appli
Texas A&M - MEEN - 357
Lecture 16MEEN 357 Homework Solution11. Problem 17.3 of the textbook Solution: This problem is essentially the same as Problem 17.2 that you worked on the homework for Lecture 15. You are asked to evaluate the integral I = 2 ( 6 + 3cos x ) dx0(16.1)
Texas A&M - MEEN - 357
Lecture 17MEEN 357 Homework Solution11. Convert the following initial value problem to an initial value problem for a system in normal form3d 2x + 5x 2 y = 0 dt 2 d2y 4 2 + 2 y 6x = 0 dt dx ( 0 ) x ( 0 ) = 1 =0 dt dy ( 0 ) y ( 0) = 1 =2 dtSolutionS
Texas A&M - MEEN - 357
Lecture 19MEEN 357 Homework Solution11. Consider the following nonlinear first order ordinary differential equation dx 5 5 x = tx 3 dt 2 where x ( 0 ) = 1 20 (19.1)a. This particular ordinary differential equation is one studied in Math 308. It is kno
Texas A&M - MEEN - 357
Lecture 20MEEN 357 Homework Solution11. For a coupled two degree of freedom vibrating system shown in the following figurec1u1m1k1f1 ( t )c2u2m2k2f 2 (t )the equations of motion are m1u1 = c1u1 k1u1 + c2 (u2 u1 ) + k2 (u2 u1 ) + f1 (t ) m2 u
Texas A&M - MEEN - 357
Lecture 21MEEN 357 Homework Solution11. A crazy man jumps out of an airplane over Aggieland. In the coordinate system fixed to the airplane, the ordinary differential equations governing his decent ared 2x dx dx dy m 2 = cd + dt dt dt dt and22(21.
Texas A&M - MEEN - 357
Lecture 22MEEN 357 Homework Solution11.You are given the ordinary differential equationd 3u d 2 u du + 2 2 + + 3u = 0 dt 3 dt dt 2(22.1)Utilize MatLab to solve this ordinary differential equation in the interval 5 t 12 subject to the initial condi
Texas A&M - MEEN - 357
Lecture 23MEEN 357 Homework Solution11.Consider the four degree of freedom vibrating system shown in the following figure.u1m1k1k2u2m2k3u3m3k4u4m4k5The equations of motion of this system ared 2u1 = k1u1 + k2 ( u2 u1 ) dt 2 d 2u m2 22 =
Texas A&M - MEEN - 357
Lecture 24MEEN 357 Homework Solution11. Determine the eigenvectors and the eigenvalues of the matrix 1 1 2 1 5 2 6 3 A= 5 2 5 2 10 5 10 4 What are the natural frequencies in this case? Solution: The MATLAB script clc clear all A=[1,1,-2,-1;-5,-2,6,3;-5
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