Question

4.- (25) Find i(t) two ways: a) in the time domain 6) using the Laplace Transform ilt) + 10 cost Volts 12 lovelts 1H I

Answer 1

Find ilt) in tuo ways a) in the time domain d) using the haplace domain i(t) 10 cos(2) 1.2 10 volts. (1+ + 10 cos (+) ilt) + dilt) dt. Therefore integrating factor eride e Multiplying to the sides with the integrating factor we get ét dilt) loet + 10 c0s(t) et eti(t) + dt. » /dlet i(t)) - foet d Jio cos(t) et etical 10e f 10 cos (t) et dt. + Now t te sin ( t) + / e *cos(e) dt - sesin () -/et) sin (4) de tres cos(t) - fece cenit) dt. C Scanned with Se+cos (4) dt = {* [biu (8) * cos(a) CS CamScanner

:etiti 10et + 5e + cos (t) + 5 et sin (t) + C. because initial ei(0) exo=0 10 + 5 + C. C-15 . ilt) 10 + 5 cos (at) + s sin(t) is et ob) using haplace Transform. (A + 1) I(A) = 10 10 + 1 10 I() = + 103 (3+1) (A²+1) s(at) A BA+C + (sti) (st+1) A 1² + BAR + CSABA A + B 0 6 + Cool and A + C D . A + Btc 0:51 B70.5 A =-0.5 = 0.5 16) (52 4 5) + 10 + A+ +1 10 + 5 cos (t) + Sain(t) iset ,(t) cs Scanned with CamScanner