MT2S - Problem 1 The switch in the circuit drawn below has...

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Unformatted text preview: Problem 1 The switch in the circuit drawn below has been in the lower position for a long time. The switch transitions to the upper position at I : 0. 6 hua + lO + v" A . F i n du , ( t : 0 - ) . + /e Ua( C. c/'q o^\ /o tffiil.) 7r': /a|r\ B . Find u" (, : 0+). vL Cc.+\ = t - . C o - \ C , Find u" (f -+ oo). {,: = ?-v 6E crtt Ca uc G-\ = ./c> t",< +Z-K\ V / ?E \ D. Find the characteristictime constant that appliesfor t ) 0. = q R ,// 4 t< = z.v L7 c-\ A.t (- (.te.- t k 4.* .> = z-? x .J * ./o <.o^3 = Zf E. Find u"(/) for f > 0. t-.c : t-*C-\ + L-.(!f\ t /2, .h.' r--o.1-1 e_ J ^z (a ;'\ Problem 2 A. Determinethe Laplacetransformof the function t] f (t) : fcos u(t - n) . = = -7Tt - c.r .r ( 1 e oa -o + aA 4( e - z- \ (t-z7.) ,,- (C^zz,-) F(r\ = -e- + f | :. a /<*^^ryFl4 tL'+ t--._..-\ , t -f ^ ot B. Determine the inverse Laplace transform of the function ^\-/ n/ \ 2s2+7s*3' laa tL f2 |f \ Ze + I + _4 .r+J ,4= -2_ (- *il) t =2 z, -3 -{ .f <n /^ (e-., '.-r\ Ft - .f=-J -r + = 3 .r I/to i= Cr\ ?./r .|l +3 +1 (+ )= | -2. -t e- :- + *;t-l ,-L*) Problem 3 A. Determine 11(s) : uo(s)fu,(s) for the circuit drarvn below. t/s + v* --+ * .c-t e= z'//(**"\ + ,r ? L, (++ A Zt r 7 .1-+ 7 6.r * ?a 8.r' + ? ? b I g-\*_-f, 6 t + trr' Ltt 6,r Ltz ?c.F q{L r + +Qr.r- +7 ?tL ?r -*t Z"rL+ +7 a? ,/1 = 2- ,/e.r- + /oa + 3 B. Determine the poles and zerosthat apply to f{(s). y' o/-- /o e t + /ot ? ? o -2. ?^rz r 3 -r f ,J VZo ?e-.n : o o -t", Problem 4 Determineu"(f) for the circuit drawn below when u,(t):26(t). /^s <do-, 2, I + v( + -c I t-^- (v\ ? t.( C''\ J f *+t+ -Lr L z J^z +- Lt+ ? (n +- /)' r-* (t \ -c g 1.\n t z-,-(e) ...
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This note was uploaded on 05/24/2008 for the course EE 202L taught by Professor Katsouleas during the Spring '08 term at USC.

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