Question

Given the following information about a 2nd order transient circuit, solve for the coefficient Q2 in the capacitor voltage vc (t) = e-Sunt in V/52 --WnV52-1 + vc (0o) for t>O. + aze C = 3 mF Vc(0+) = 6 V Vc(infinity) = 6 V ic(0+) = 2 A Wn = 26 rad/sec zeta = 2.02

Answer 1

Civen that (t) = e-sunt care con + ag 6 Wn13%) telo) (O) = 2A, con 26 3=202 Ce 3 mp Vc101) : voll, Velo) 260, we have to fond az Now the use we will given boundary ceman at to find a t: + Vec09): é o lar ewn 13%'t a ) +! wn²1 26 2.01-1 45.63 6 (ai 45.63 + a22-45:68) + 6 91.24 ܕ ܐܐ -Tee-51.26 Nr we will be fels cdult) dt [{qun e-3wnt (s, ewadzy at to f(0*): -C3Wn é ' [4 245-43 53245.67 ' ] 2 = - 3x103 * 2.02 x 26 [<, e95.63+hé -45.63 *5) 4,645.83 -45-63 +20 < : -1 2-69 45.63 4563 = -12 by putting the value - ze 21-26 +2 c-45 Laze 45.62+ de 6-45.63 -1201 AD ملا can see Can not that the R2 term get's cancelled out so Calculate Tz reperately. we