Question

For the underdamped circuit shown in the accompanying figure, determine the voltage v(t) if the initial conditions on the storage elements are i_(0) = 4 A and vc(O) = 10 V. il(0) 2H] v(t) 50 Tuco) 1/40 F Please put all numbers as integers. Click here to enter or edit your answer v(t) =

Answer 1

Y ELLO) 7} I velos 52 = Velol in Laplaca (ها قوامها راي =274 = ( ن )LI (4) 2م 1- LS = 2S - دا ا و (0) لا s/10 ( * 10/s لم | 52 الا 2s Potential of a node ' va = V(H) by KVL at node a Va+ 8 Nava-lol 25 * 5 54020

C va [as + 5 + 2] + +=0 va [ *s * *]= -imo va[ 20** *5.52] Seseo va[ s +88420] = 4 pes (3-6) Na [82+88+20) = 10(8+16) 10(5-16) Sa+88+20 = 10 (5-16) $2+88+64)2(4)+20 va = = 1015-16) (5+4)?(232 = 10(8+4-4-16) (s+43²+ (2) ² Va = 101 5+4) (5+48 + 22 20x10 - 0 (8+4)? (2) 2

inverse Laplace transform 10(S+4) = 1o. ett Coszt (S+4)² + 22 20x 10 = 100 ett sin27 Putting value in equ ® = 10e4cos2+ -100e4t sinet - OR loent (Cus27 - 10 Sin2+)