Question

4-(25) Find i(t) two ways: e) in the time domain 6) using the Laplace Transform + 10 cost Volts 12 lovolts 1H

Answer 1

ilt ti lo lost v ir 1o.v. m TH for tro kula 10+ 10 cost i (t) + 1. dilte dt o i (t) + di(t) dt 10+ Lo cost first order non homogenes can dilt + ė (f) 이 t Lo + Lo cost Compare dilt It + pilt) Q Sot I.f. Spat е e et Q-- 107 wst ix If = jQxI. f. at exet 5 (10+ lo cost). et at

j.et. 3(10+ lo cost) et de t. Schoe t + + lo et cost ) dt lo et + sloet 10 et wst dt Let t I - Si la e cost dt I - t bole. [+ sint] Set (tsint) dt 1 etsint - { et [cost] - Set (=cast) dt? et sint + et cost Set cost at I et - I il sint +6 st) 2 I et (sint tlost) - t (sint + st) I e 2

Io + 5 (sint + lost)+cet i et 10 oett 10 e (sint&lost) +C 2 ict.

at t20 ilt=0 10 + 5 + c CE -15 ilt) 10 + 5 sin t+s cost-15e-t

5 Lap lase method - from ean 10 + Lo wst eit) + dilt) dt taking Laplace both side I (8) + 8 IU) 10 + U ele set IB2 = lo + t 1 St] ( S SL +1 5 - + 10 ( 5600+1) ca com 8 +)) (84+1)

118) n s2+1 tse (8+)) (0) (82 +1 ) Ico) a 208? + 10 (8 +)) (5) (x2+1) take Partial fraction- А 2082 to + A t coto 82+1 B sti (5+1) (82+1 8(8+1) (CA+D) +3C%2+1) 8+(841) (91VA 808 +1 (8271) Compare ean 20 8² +10 = das(A++c) + sh (A+C+0) + SCA+O+O) +A A+ BEC - O At.cto = 20 At Bto = 0 A = io on salving tha we get A: 10, B2-15, C5, D=5 10 2082 +10 $(8+1) 682 +12 15 B+) + 5845 82 +1 8

15 si I(8) a ela Lo s + st 5 $2+1 s 82+1 take Laplace inverse both side # id) 114) 10 - 15 e eitt + 5 costt 5 sint ilt) = 10+5 ast+5 sint- iset