Chapter 8 Solutions - Soln0851 051022

Transcript

Chapter 8, Solution 51. Let i = inductor current and v = capacitor voltage. At t = 0, v(0) = 0 and i(0) = i o . For t > 0, we have a parallel, source-free LC circuit (R = ).  = 1/(2RC) = 0 and  o = 1/ LC which leads to s 1,2 =  j o v = Acos o t + Bsin o t, v(0) = 0 A i C = Cdv/dt = -i dv/dt =  o Bsin o t = -i/C dv(0)/dt =  o B = -i o /C therefore B = i o /( o C) v(t) = -(i o /( o C))sin o t V where  o = 1 / LC