Question

Given the following information about a 2nd order transient circuit, solve for the coefficient ay in the capacitor voltage ve(t) = e-Swut (@j sin(wat) + Q2 cos(wat)) + vc (00) for t>0. Wd = wn/1- C = 10 mF Vcl0+) = 2 Velinfinity) = 7 ic(0+) = 1 A Wn = 62 rad/sec zeta = 0.04

Answer 1

(x, Sinkodt) tag (og fodt)) 0 - Gout Vect) - e زمره) با + wala on 51-8² c=louf v (otl=24 U (as) = 70 iclot la Wya 62 rad (sec LA Zela 2 0.04 wd = wyr 1-42 625-66.oyje wola 61.95 rad /sec

Votle zu put t=o. in equation O. votli e pai a, sino t q casoy tulos) 2 = 12 + 1 12 = -5 . i Gl= c duett) at differentiate equation o -Gout we get du Ct). dt -Gwat oda, e as welt - Lz ad sin codt - wne" (a, sin wat tolz cas wat te अ educt) at

POCO ical agence surely sin coat the eag wades { wda, -Gwynt fee Cas wat ada2 sincede It icotl= 3 1 = -0.04 X 6 2 X 10 X 10 qa, xo + q } 3 + coxco 26169 61.95 a ང། Oo61950, 0.0248 xE5) + 1- x = 1.414 Ang