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ese271-4

# ese271-4 - ESE 271 Final Exam Name Spring 2011 ID Number...

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Unformatted text preview: ESE 271 Final Exam Name: Spring, 2011 ID Number: Each problem is worth 20 points. Do not write your answers on this cover page. Prob. 1: Prob. 2: Prob. 3: Prob. 4: Prob. 5: I) 1 a Prob. 1: Determine the single cosinusoid Ac05(5t + Q?) that equals 2cos(5t ~ 30°) + 3sin(5t + 45°) 5...; ’X : (104(7“ 90‘) Pliv4J‘oR I: 2(‘306 1- 31:13:30 2cm(.3a')+ 3 m Gum—a) +J‘ <24.“ (—30-) + 3Mf—e-s‘ﬁ) : 3.353 —J‘ 3./2/ —3,/2( = Juan 1‘4“"???3‘ r 4% 9F? Z.~3 9: .- 1+. 9:9 cw (it -39") Autwtk — (00 (b) Prob. 2: (3) Determine the Laplace transfor (b) Determine the Laplace transfer fort < 0.) 2 F“) m of f(t). (That is, get F(s) : L f(t).) m of the generalized derivative df/dt. (Assume f (t) + #(t-ﬁult-Z) — 2(2‘v3)u (#3) {(2‘) : 2u(t) ‘Ztll(f) 1L ~24. 2 -3}; FM) = 1:2— ” '27- * ea — —-—'""e 4 A 261 if: : 20‘“) -2q(f)+ 4uH'1)‘ 2u(f—2\ cH' 0” am. (if: 2—3— + “‘9‘”_ 263‘ ' 4 A. A: :0 Prob. 3: This circuit is in the AC steady stabe. Do a nodal analysis to determine the voltage v2(t) 1‘5 a. cosinusoid. 17 (t ) 72 ( t) Iﬂ. Fﬂﬂlam CIRCU’r,‘ /JL INSID£ BALI-001V: V,-V2 32V, J V’ ;_V? K54 on THE aAuwu: V. v1 ,. "‘5 + M'- «- __ .. 0 -w. I 2 J7. "J 2 V2 + V7. : \$- 5 Z 3. ° I-JZ 2236 MU +5143) Prob. 4: Using a nodal analysis, ﬁnd the Laplace transform Vc(s) of UCU). 'Write your answer as A polynomial in 3 divided by a polynomial in s. I H (Hem 0< 2‘ <00 (1(04') : lA 7{(0+) » /wlz In TIME DONG/N: rial-(ff) A46” 5 0 l f( ““06“" _~ 452+) +C at + ,d—l TL “GM- z=/, c=/ PPLy L‘: z A ’ 42 A, S’DLVINC Fan Vat»); Az—A M A 2‘ M \4( ) 4‘ +123 4% FHRHEP ClRu/T’: S "“N’ V“: r14: TRANS —-——-' 4N9TII£R Nut LA: vch‘) J” I la Vt») NoDE .' kc; AT c ,1. ch) +Va°§=0 V(A)— A, + _L. * 'l c c A k“ l ’o ER. ANJ'w ,5 6,457 THE 5AM \$3Lvo~£ FM. V‘JM) w in, ca [T u ANJl’ann I 6» , SOLUTIO’J! (/55 A» Evan/AL; 7 rn Sr/L‘ AHpTuén vrl") A / I J— —1 [(CL ammo, W + Va»: 4 van) :0 A 4., I E Tm: YIELD! rut J'AHE A”"" R' Prob. 5: Determine the convolution of g(t) : e“‘u(t) and h(t) 2 (cost)u(t)‘ That. is, ﬁnd f0) = 9(t) * W). W A" H4 at f phuLA, GOD: I ) Ha») ;: ”7—— 0111 77y: Ext: A: a A A + K + K“ .. A) = —--——-—--——'—~““‘ = _.._._.. _ ”- FM)- Con/Ix A+I)(4-j)(?°+j) A“ 4—, A“ ,4— "' _, -: «=0, ,3:/ _ A“! [Aw « z I<~ A -.-._l.—..= I :1 —zfr° (Mo/4+1) L- (wmﬁ 2m) 25‘ l J "1:“ k=-‘r: 5'.) - _°(t ”)"J'Tt‘I-ZKe w(t+ k) 1 - I H“ : ‘F'8 t + :5: aorta—95') ANOTH‘" y°“’7”°” ~‘ V}; 77w! Cam/“LINDA! z~7£4R4L: 2‘ ‘ “f): t ”(f-x) J — 9“]. e" ELife 4x 70?}: f0 5’ cod-x r - O ‘1 -t (11771 [2‘ G ('"J)"{i‘] - 5; W. + , .. 2 [+J a "J o e" [-__L__ ~ ___I__ _, «L‘ eteJ + 1 eta-Jz‘] : 2, "+4 l—J' I'l'J I—J ...
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ese271-4 - ESE 271 Final Exam Name Spring 2011 ID Number...

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