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hw_1_w06_soln - l—tH—ldb—Eldldb 13:22” P'llzL'H#51...

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Unformatted text preview: l—tH—ldb—Eldldb 13:22”: P'llzL'H #51 HtHLl IzNLillelelNLi b'l’d titl-fil DUHU I Q? @ it» it! 123 ' it“ 3211 Lu: Homeworkrfiet #1: MAE 3600 — System Dynamics, Winter 200359 Due date: Friday, January 27, 2006 Problem 1. Complenlhmherz is z=-4.82—j3.41 a) Express 2 in poliar form (magnitude and angle, in deg) ‘ b) Compute the magnitude and angle of the sum, 3 + w, where w = 622+ 12.914 1:) Compute the magnitude and angle of the product, 2w 1 :1) Compute the magnitude and angle of their ratio, z/w Problem 2. Comptaeflao) using the Final Value Theorem (PVT) for the following functions where f (be); ists. Compare the FVT result to the simple limit flue) computed with t -1 no; (again, only where the limit exists). (2) a) f(t)[email protected]—-3e‘“) (I: h) f (t) = Bailifeos 41 0) f(1‘) = 0' 5 + 211-“ 1 2e" sin 3: '2: :5; d) f(t)—03§(1)+2e'“ Problem 3. Given the ,haplace transform: 4 9,11,): 1(51 + 9)(s +1) does f (co) exist? Explain your answer without obtaining the solution flr)’. H Problem 4. Obtainlthe solution x0) for the following ODEs using Laplace transform methods and sketch the solution 1:0). 192.: a)Jir—2x=3,;-9c(0)=—l .1.— b)s+9x=o,rx10)=—2,1(0)=3 g e) 2,51,12,31,an x(0)=0 3'c(0)=—2.5 _...-"" TenthOok practice problms (not graded): B-2- 9, B—2— 10, 13—2 13, 3-2-14, 13-245, 13-2-17, B- 2-19, 11,12,122, 3-2-24, 13-2-25 , FtH—Ub—EUUb 12=ab - - . _. _.___-_|_ ________ ML 0&M_J__Hw$ ...._._..J _ (DEW [a] E": mum III comm i‘flm WEN: WW W-N-r! www- van“... 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NtEH & HtHU tNUthtHlNU ij HH4 DUHU F.MY ___.______ ' q_,_,L_.,.m_.J_- __.._,__......_q_..w..,..‘_w -.-_W.._._..__m....J.W mt’mw) h a) ZXFF [2 )5 + MIX -'- -4— NZflfi d: , )EKO)='"‘ 2L4— g l lzzfii} -.-. giszXf-O _ w)“- my] ,, F3 main?) 9 “fg-yzgszm — mo] : ESE?) w 10,:ij mfg) H : .2. _ 4. E? 303%.] = ‘ Fat“ i g? zs'lXEri'h-gr; ~4— MEX—(J) + 1017:) JEEQ ”r 5-“ {fir-“Q r..- ~. ._ 5: ‘ DJ! m9 [2+2 + m] r ,i ~§ .z: —4 ; KG) 5 “555"” 4 = 3L +- r-w ‘ 23(32 + £3 + S J 3 ) : fli _ ~cm4 1‘ F10 Id: ‘ C / 5'1 1+ 512 1(5) {1540) : :3 H CJ-/2§- F. . 5: _/ ‘ a; ._ 3(1) {:+§~)/ _. 2/ : 952:5,“ 5 =4: 40 \ N $0.4 w . . ‘ 1‘ 5-?" X0): .«_,_ + o (a; + a 3:25“ 5 5+! 5+3- . _ ,-, 54,? -1: -51» ; x6e) - a8 [31%)] = #@a% ~ 0.22? 2 ”+0.52% h I a TEITFIL F' . IZI'?‘ ...
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