ese271-3

# ese271-3 - ESE 271 Third Exam Spring, 2011 Do not place...

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Unformatted text preview: ESE 271 Third Exam Spring, 2011 Do not place your answers on this from: page Prob. 1: (10 points) Prob. ‘2: (30 points) Prob. 3: (30 points) Prob. 4: (30 points) Name: ID Number: Prob. 1: (10 points) Given f(t) : e’muﬁ). Thus, 13(5) : l/(5 + ‘2‘). State the Laplace transforms of the following. That is. ﬁnd the explicit, functions of 5 cor» responding to the following. (if/alt as the ordinary derivative for U <:_ Z «i :x. (Ignore the jump at f : O lII flt‘f; (b) (if/dt as the, generalized derivative for 0 g t < oc. Include the jump at t 2:: 0 in fUi). (C) fit “ 2) (d) [0‘ f(1')(l;z: (e) NM -2 t I: —2 (a) «(if r — 2 G W») 2 d’ A + -2 z A _ 2 m A (A) :1): 5 arm ’26 W ’ Mg * M2 :22“ .494 (a; Q A +2 {as ’ 4 (A 10\$ (9) ML» Prob. 2: (30 points) Find the Laplace transform of Mt). Iv r916 77h: DobMWN! or f. M 2 -+ C’L‘fp [IV/‘n/F 'i’ “rt/[3+3 “‘ 0 2’ ii 5‘: +H Hm» +4 ‘0 J? + ‘1" APPLY 2:! gr 2 M‘ :5) (Ala?) +<“I*T, ‘54 3A»? 345'? w ,4 ,,,,,, W, I = - ' M2" A2+54+6 (4+1ﬁhc-os} A :- —J’ z 5’ z // . ﬂ - z - 5") aft} 5 «69 2 1.1/9 5” ’ r, J (/fé/VIT: ANO‘YQEK uncut Tramway», r” Prob. 3: (30 points) Find vc(t) for O < t < 00, when vc(0+) = 0. Here e(t) : u(t — 3), as indicated. 2.0. I %(0)=0 + em = u #3) GU) 11;”) .1. F ( w“: - 4. 73.3, eff/=0 7’5:- "0) 8(1) :1 forfei 7RAA/5rdnné o C(ﬁcu!1~; 2 Em ~34 Eu}: : 30’ 2 2 9‘3): A(4+2) “ELM v 441 .,_ MEL ADM?) A A4»? A ' I ) 8: ~! 77‘”: «In — —. 9“”, w 1 C > - .4! (twin? “’2‘” 3 “(NJ «4” ﬂaws) Awmm \$owm~. I} TRE Tm: Damauv. “<5” :31,“ J, chew) KM '2 + ‘+ at " APP Y ’5’ L KALZJZL” + J-(A V620,} - 0) -: 2 ¢ 34 / \ (3‘ \é/A} z' “igfﬁil ) 5(4) : ‘ ,1» 134-2 2 -3 , k a Ca V (25) ’-‘ C’ A ) ’7‘ pm”, ‘ Prob. 4: Determine the inverse Laplace transform f (_ t) :: F(_s) of i : , (‘5') (s L1)(\.5 r2)3 8 8 F/A) : ’4 + :3 -+ 2‘; 4 A+‘t (A+2.) /A+z) A: ~41 .u _ J. (A14) {/5 r“); ' a t a J. a, = w; - 2 A4“? Ar»? w J 5 ;~ _ JAM 82‘ d”, A+‘#) A”? (Ax-(m)1 A“? ,5 3: ii: w—L-«m I d/ ,:_’__, 3 2 B 45*“ 4:4 ‘ 2 4» «MM 5;) ‘ix / “gr ; Z” “2% “if/8&2? {gi;‘:—g;€ +«i’3-e ’54 , -w 2” ~11 t «2: 4 ...
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## This note was uploaded on 09/26/2011 for the course ESE 271 taught by Professor Zemanian during the Spring '08 term at SUNY Stony Brook.

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ese271-3 - ESE 271 Third Exam Spring, 2011 Do not place...

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