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ThirdEaxm_f03_new - ESE 271 Third Exam Name Fall 2003 ID...

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Unformatted text preview: ESE 271 Third Exam Name: Fall, 2003 ID Number: Do not place your answers on this front page. Prob. 1: (10 points) Prob. 2: (30 points) Prob. 3: (30 points) Prob. 4: (30 points) Prob. 1. (10 points): Find the Laplace transform of the following periodic wave. 7C“) 2? .._ (0N TINUEJ PfrrtabJCrV—‘V 01V 042'400 Fore 0<t<=L Ht) = 2am —4’-u(t-I) + 2aH-2) 2 ‘1‘ _A 2 -2A "'3“ 33-9 + 36‘ $1,, FK'A) :- [Fl/t) ._ __2__ 4 "-4- 2 -24 I A 3:0 +:8 )“fg—ar’“ Prob. 2. (30 points) Find v(t) for t > 0. , t) a“ I’V'(0-I-):' 4 V FMS-r ”Fm”: U-“F 3‘“th 3:; méufifi'fiil '_E£L:J¥J:.;}j”— “"_'_”—— ————~~-_ kc" JKf)“ ’ t ' I «I — —-— rv/xh/x +— £/9 ) ~— .3: 2 £3 *- + 2 42‘ £0 ”a“ 2 V 6 I :- “'-- + —-— J A. _ vat’é’) 2A .b- + 1( y 4) I V(E:’ + g I: l‘ 16. +2 Km. «I + JL + 6 _JL __ fl 6441 24 7;" 4" 2/ 2 __o . VII/J (,7sz: = 44.4w. A 41+; CguTrNLI-F A-r_ nu F‘W‘EE _Hérgfufi ___ _ ___ Amarag'n “Suit; ""9" __ » '6—2 . *5 V“ 6’5 !1__ = A. + A I A: _{___._.L._.: 3+‘J =J31+61LL;_:{_ ~ (X'J'MAU) 2.1:; Ah} 2} S” °” W“ = ’3_-_‘:’_6_9r°__(*.,f ”eff?” /E.-n;an :fiLuTeaw u “gun“. \ I4» Appélca‘rrov of 71w" F§NHUJ,i Far: 7/“: (oi/NE a? H J‘UH 0/"- 7—590 Apfitéd 3mm: way Au: 7“ Jam? vl-urwr», Prob. 3. (30 points Solve the following convolution equation for g(t). : [0 mm: _ may; 2 w(t) where f(t) 2 F“, 111(1): sin2t, and t > 0. APP“; £5 __._"_.__.—- C(43) :— 12 A44; ’5‘ +9. 2‘4 1’2. GKA1 - -~ + ': 2 A + 6 2 ANN»: £4 ’0 +‘f ”2+4 A1+‘+ Awe-{56:2 301.9710”: 2 I Cf/fl: [5+1 :— L + A“ ’32—!“ A-J‘? A+J'2 (Ht/1 - A= J = i513.— JIM;2 3m: 2% 3.252 m0:— 7N2») = 6. 324 can ('2f~7/,r74) (fig: TR»: Seku'flfiddi Area: 7y: SANG) Prob. 4. (30 points) Find the inverse Laplace transform of 32.1- A’M— 211+; /S’A3+é/s’ ax: +4 3,03 +505: 4-34: I M -44} +51- FZA):3«O+ ”¢41‘-‘¥_fl : 34+ «444-4 A1+?A+t (Af-Ijz : 3A ‘1L' A —.———. 1- 8%.... [23+])! ’4“ {Em-*{W Liv-‘1 1.1? H ’5' fit“. }‘CL_‘? f3? 41% .fi: J fia-J l-O’L" ’51 . r3 if/A'I = C? + 8 ELM-,1? 15*; ”A”: +.—;+5 L lard; ...
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