Question

4.- (25) Find i(t) two ways: a) in the time domain 6) using the Laplace Transform t=0 sec + 10 cost Volts 112 lovelts 14

Answer 1

Solution ict) 10 V alone 112 in Blic"] 10 Colt Volks Tec Jou ict) : 10 [1-0' for 10 cost alone. 10 COSE 3 il dildo dt 1000 . 10 Cent ** ca di i(t). Um VREAU (collot- d) tee -4/2) W = l rad, taul(ene) {cos A-95) 450 (+)? it?!/" too, ilt0 -2 2 [cos 454)+e] -C094 ZX it ilta the [600 (4-4c") - ha et] one ['cor (t-450) -set) toral cierreut ilt) = 10[1-et] + C08(4–45°) - sé? 10+ 0 cos (t-us)-15e 10. [est cor eso teint sim 454] icti = ilt) S2 i cl) = 10 - 15e + V2 7 10- ise + 5 col + + ssint 7

ty and form, 12 12 10XS + $2 + + Slov SL 5X1 ΤΗ 1.632 10 -lo 10C 527) $2+1 ) 105) 20 (-1)? tio (6) Laplace ict) LOCOSH 10% Applying KUL + I (s) + SIC) 0 3 (!) (+1] = los 10 SCS72 (sti)(2+1) 10 (52 +1) cios (51) 's (5+1)/5241) I (5) 1052 4 10 t los 20 s? + 10 SCSH) (52H) s(s+1 182 +1) 2012 tio В SC8+2 (2H) + CSAD SH. .S24 2052.410 = A (5 +1 ) B($+1) + B (3 X6271). 465 + b) (s(5 + ] 20 (99 +10 = A (oh) (0+1+ B (0) (0+ 1) +Co+D)(016041)] brzy putting [1:8:0] A com 26-1+1) +86-761 +1 + (0611+ D)) ELH) B = -15 my putting =1]. compare s2 coefficient in ego 20 AC D compare s coefricies in ego - Ait B t D 1-5 from ean ② 20 2 AACAD 20 = 10 + 75 15 CES + 5 S+) 5241 52+1 Apply ing inverse Laplace itt? =(0-150 tot 500st 15 sint). ME) 9 1 A = 10 :: I() = - Framfommation t we get .

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