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q5s_sol - NAME 39 Lu‘r.oN Unified Quiz 86 One 81/2” x...

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Unformatted text preview: NAME 39 Lu‘r .oN Unified Quiz 86 April 22, 2004 One 81/2” x 11” sheet (two sides) of notes Calculators allowed. Calculators may be used for arithmetic only. m books allowed. Put your name on each page of the exam. - Read all questions carefully. Do all work for each problem on the two pages provided. Show intermediate results. Explain your work --- don’t just writ equations. Any problem without an explanation can receive no better th n a “B” grade. - Partial credit will be given, but only when the intermediate results and explanations are clear. Please be neat. It will be easier to identify correct or partially correct responses when, the response is neat. Show appropriate units with your final answers. Box your final answers. Exam Scoring #1 (25%) #2 (25%) #3 (25%) #4 (25%) Problem 1 Name So I. u T 1 Q U A causal, LTI system, C, has impulse response g(t). The Laplace transform of g(t) is 4 0‘9) = 1. What is the region of convergence of the Laplace transform? Explain. 2. ls the system stable or unstable? Explain. 3. Find g(t). l. Syslfim lag: 130/93 G) 5: '1 Gama?! Sr-«B‘ Br»? Cflkaté CZ % (35191353,, Wu‘sl" 40 "MN; o-l flj‘L‘leS'i [ital-e. 39 m Ram... 25 Refs] > -/ 2. TM Rio. 6-. c0 altalw s it is Sic:th Re 2: C). TnL‘Q’Q'fia/‘Q; ’P Jr Dc: CA Patr'lclal 7(‘VQL1LI‘0L-5 expanI‘OML ( 3 .1: q 3 ) .__ 0~ + 5 1L c, ($40841) S4»: CSHJL 5+3 I U343. Love/up va.9.+L\oc)\ +0 ¥wl is (f b: “L 2: 1:2. 3+1 3:4 1 C: ,5... _ H : <5“): “‘3 ' L-zfi Probleml So (SM) (5+3) $4»: (5+4) ‘ “FLU; 1'} 4am“, «(for a” S, so f’Mnen I" = a L 2. 4_ __l__ ILr 3 I {'1 3 1‘7 a = j .— 2.--.!_ : —/ ‘5 3 :7 0(3): "’ 4r 1 4.- ‘ ‘5“ HH)‘ 5+3 ) so +14 lav-UM J "5 5+2, CA‘ 5'70 RE} 7'! Problem 2 Name 50 Lari ou , Given the signals g(t) and u(t) as plotted below, find the signal given by W) = 90‘) * W) Sketch the result in the grid below, as accurately as possible. Be sure to label the axes of the grid. Explain your reasoning on the page that follows. 2am 2gm I ’ 101.23t 0123t III-IIHIIIIIII IIIIIIHIIHIIII III-IIHHINIIII III-Ilflflllllll III-Illlllfllll IIIIIIMIIIHIII !!!!!!HIIIUIII.t III-Hmlllflflflll III-IIIIIIIIII III-IIIIIIIIII IIIIIIIIIIIIII III-IIIIIIIIII IIIIIIIIIIIIII III-IIIIIIIIII Problem 2 U51. 2 5/241 +9 do Name M COVH/o/U-HOM I Z T -2 -1 O ’2’ So jlf“’t) (5 For O,- f £_’/ 2' l‘S V‘o ouQV/0.F l 0%- u(/C) X, j({'c)/so 7(é):o i2 t—l -(; L Do Seat/a, values 04 t: f : o alf'f) jif—fi‘hfl'f) *I’lL fi'q arearvU’Lh‘z .mwm WM _ WWW-aw... 'L"0 ’1' —\ Ir iii-L" file—flak) ‘” 2” “‘1 megajmac 5W ._ Tamar Problem2 Name 6,2:Mrlou S/MiIAVI) (3(2): (-aJ 3/3); SinrQ u/ :7 4M Piecemé‘fie (OHS/fiwf/ y (‘5 Piecewia “max mad cbm'l’inuoug, SQ 71%) is 615 -$L.OQJM "" WLI Problem 3 Name 50L Q I [OH Consider an UN system G with input signal u(t) and output signal Explain why knowing the step response of the system allows one to determine the response of the system to an arbitrary input u(t). You should do more than just give the equation for y(t) 7 you should explain why the result is true. AV‘ arbi‘l‘fav‘a Sijnal ul—t) an“, b1 qPProximHeA arbi-i’VWHg we.” 6&5 a Saw a; file/“yea! anal 6C}_Q|~Q_fil Elfifij a) SL099!!! la fffiMNl (TM. (11%) shows/n [4a) a (JilS C‘Ow‘llt’luii‘j a {7:13:0- Tl’ilS l3 V104 fleC‘GiSfi-LVVJ .9), HQ; awfuwm‘l‘) U i5 G‘)r'0X7-aie lu TLi-Q Caa be {Out—Lg” [9:] Safe/Posi'l'iom/ $1}ch *HxL s/g-Mw, l5 like?“ (1an “(lme invawmm-l/ and (AA [Chow TL; 5 ijfOW‘S/Q,’ 4: Vi i0) 75 ‘l’ E— “ <?m—I)]j$(t'fh) n:l Problem 3 Name ML— beaomes fat“ (nu/rah am} “UN-L ra‘HO lance-was a Ae/iva4iv4/ so 00 glf):j$’f)U(o) 4 ] 01:1?) 35 HAW/z o '2’ DuLaN,"$ {:Lgfifii expresgrs #4 res/Dona £0 am 42L2+ij [MPH— [m %e./m5 o! SR}; VesPomge, Problem 4 Name _5° LOT l QM Find the step response of the circuit below. The component values are C = 0.5 F, L=1H7andR=3§l “(17+ 1 /L5 L5 R y(z‘) ---—- 4- L/LH'): U 65 I yZ-(r): Yejf and m Cow/90.444471; [mom im‘wdamcéx as shawl TLJLM ’H-ui. +quS-LQ/ “QJHC, +J|OH (l S :3 (r15):- R —- y M IZ+L§+//C:; Since M cfrcqf 25 a [Jo/+67} chad/u, 6(5)“ RC5 WW LCSW+PC5+| : w{Em/L45 __ 35 *Mm SI’H'E—S‘F—L _ sz+35+21 Problem 4 Name U T J {L +LUL mind i;- a w}! 5M0) “WWW”, 4ame U(g)= //‘S (Ema). TLAre'éMe/ W5): G-{s)U(3) : 6(3) 3 3 5 51+ 35 +2 T; < ‘(hl (“46/ [I L14) [S+‘)(S+;) L‘— 3 __ (Pa/41¢! Lick('l’!\3m3> S+\ 5+2 13%ka «Ha 533qu is caqgafl +1225 (‘w/D/ieé mm».wmwmmmm.uww .. ’2 ‘4. .. ...
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