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

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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. A. Find u,(t :0-). + v" + lO + /e B. C, Find u" (, : 0+). vL Cc.+\ = Find u" (f -+ oo). t-.Co-\ = {- ,: C. c/'q Ua( o^\ crtt Ca /a|r\ /o tffiil.) 7r': / ?E \ t",< +Z-K\ V ?-v 6E ./c> t uc G-\ = D. Find the characteristic time constant that appliesfor t ) 0. A.t (.te.- L7 c-\ = q R ,// 4 t< = (- .> = z-? x .J * ./o <.o^3 = E. Find u"(/) for f > 0. t-.c : t-*C-\ + L-.(!f\ - r--€o.1-1 J t /2, .h.' z.v k Zf 4.* ^z e_ (a ;'\ 6 hua
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Problem 2 A. Determine the Laplace transform of the function f (t) : fcos t] u(t - n) . = c.r.r (1 -o + aA 4(e -z-\ = - e oa (t-z7.) ,,- (C^zz,-) -7Tt f F(r\ = -e- + tL'+ | t--._..-\ /<*- B. Determine the inverse Laplace transform of the function :. , a ^ ^ r y F l 4 ^ ot t -f ,4= .f <n
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