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### Exam1

Course: ME 391, Fall 2008
School: Michigan State University
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Word Count: 485

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of Degartment Mechanical En2ineerin2 Where best the never .., rest MICmGAN ST ATE UNIVERSITY ME 391 Exam 1 A dominator's delight! Fall 2002 Instructions 1. Therearefive problems. Allocateyour time and effort to maximize your points. 2. Layout your work clearly and showyour reasoning. 3. This is a closed-book, openmind, examination.One3*5 card allowed. but Problem 1. What kind of equation am I? [5 @ 4= 20...

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of Degartment Mechanical En2ineerin2 Where best the never .., rest MICmGAN ST ATE UNIVERSITY ME 391 Exam 1 A dominator's delight! Fall 2002 Instructions 1. Therearefive problems. Allocateyour time and effort to maximize your points. 2. Layout your work clearly and showyour reasoning. 3. This is a closed-book, openmind, examination.One3*5 card allowed. but Problem 1. What kind of equation am I? [5 @ 4= 20 pts] Classify the following equations with respectto their important attributes.Parameters known are quantities. 2x+7y=14 -x+3xy = 0 Unknowns: X, Y m*d2xl dt2 +b*dxl dt+k* x=f(t) Unknowns:x(t) Parameters: h, k m, a2 *(OT/ax)2 =-7.S*(O2T/c3t2) Unknowns:T(x,t) Parameters: a x*dy/ dx =3sin(2x) Unknowns:y(x) (e) Give an example of a system of two nonlinear ordinary differential equationsin two unknowns. \Examdocs\Examl_FO2.doc Page 1 September 2002 29, T\~~~-4--~_. L#~W". I.II.~III. ,."1\,t".."~ ~,,..I14'..n:..~~...nn UI. l".~,-"a".'-a. ",-,lIil..""". , MTr'1.JTl-::.A N' ~T A ~ ~ TTNTV1i'D~TTV~ ~ ,...~_.. .~.~,. ~..~. ~,.. . ~.~. Where bestneverrest ... the Problem 2. Complex numbers are really not complex. (a) Let z = a + ib = rei8, [4@5 each = 20 pts] where = J:1: Show how (a,b) and (r,B) are related.Which i form is Cartesian? (b) Express 3+i4 )*( 2-i in the fonn: z= a + ib. (c) Express (3+i4)/( 2-i) in the form: z= a + ib. (d) Sketch the quantity . z = 3 . e ,(-38/2) . m the complex plane. Show . It . m (a + . Ib) fonn . m the complex plane, clearlabeling. by \Examdocs\Examl_FO2.doc Page2 September 2002 of 29, Degartment Mechanical En~ineerin2 Where best the never ... rest MICmGAN ST ATE UNIVERSITY Problem 3. Mashing monster matI"ices(not). [4@5 each=20 pts] [ 1 2 3 Find A *B, where A = 2 -1 01, and B- ~ 3J . 5 8 :1 Find B suchthat A *B = B* A, where A= 1 -2 ~J Find (A *B ), where 't ] A=[~ 3 2 and B= -1 () 3 .2 ) '2 (d) Find Det A = IA I, where A= -1 0 3 0 3 1 0 0 2 4 2 4 S -2 \Examdocs\Examl FO2.doc Page3 September 2002 29. n6""""~6n~ I.I~W'" L"""UL n" u, M6..h..n 1...""" 1".., 1 ];'nn.n66"nn ~"."""" '.'. 1\IfirUT~ 1.,..,--.,.~~1.' A N~T -.J. A ~. 'T'1j' A'-' TOOTV1i'D~rrv -.-,.. . A'-'."-,,a a . Where bestneverrest ... the Problem4. Love thoselinear algebraequations. (a) Find x, where Ax = b, with A ~(~ [6+7+7 =20 pts] 6] [1 3andb=2 ] 2 (b) Find X3 by Gaussreduction,where Ax = b, and ;.4=1 1 3 0...

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Michigan State University - ME - 391
~)~:';',:; M poh. ;-.1}~.,;.pprin&quot; &quot;~:ME 391 Exam 1~ fi: ~ !~+ ~Fall 2002A dominator's delight!Instructions 1. Therearefive problems. Allocateyour time and effort to maximize your points. 2. Layout your work clearly and showyour reasoning. 3.
Michigan State University - ME - 391
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