Question

Given the following information about a 2nd order transient circuit, solve for the coefficient ai in the capacitor voltage ve (t) -Swnt (aj sin(wat) + a2 cos(wat)) + vc () for t>0. — е wd = wn V1 - 52 C = 7 mF Vc(0+) = 2V Vclinfinity) = 8 V ic(0+) = 2A wn = 89 rad/sec zeta = 0.15

Answer 1

Given Go - Gent Vel) = e (con sinuyt It Oy Casust'). tve.(c); 670 s0 Wa= ung =59-17-18-159 Wa= 87.993 Given Vecol. = 2 v com as I eq 03 Velo) = eo l Kisino +.&COslo) J4VG es *+ 8V dy=-6 v Giren, illet) =2A Eccot) = c It avut) dvest) = icket at

TVco) y d dvclt) dt quint (X, sinust stay cosasty D x = è ewente (% coswat. Ws)+ ay sinwat. -eunt Eqwn) e A cos wat dܢ. ܓ adequate «s [ corupt of quality with -ewon't 十幽e e (sin wat S st dvelty dt 2 se che + st duelos sē (w costosowa 1+0 + x[-quin]) dt = x, Waqin G dieet) dt ico) c 2. = x; wd - Qun ay 7 MF = 27.87.993 - 0.15189166 a = 2-3367