The capacitor in this circuit is initially charged to 10 V before the switch is closed at time t = 0. Suppose VB = 20 V, R = 460 2, and L = 90 mH, C = 14 μF. B t=0 R www L + C (a) Determine the following initial condition for the capacitor's voltage drop vc: dvc(0)=0 dvc (0+) dt V/s (b) Determine the roots of the characteristic equation for vc. (If the roots are real, state the smaller-magnitude one first; if they are complex, state them in rectangular form, giving the one with positive imaginary part first and using j for √-1.) $1=-160 $2 = -4950 (c) Determine the voltage drop vc(t) as a function of time t (in seconds), for t> 0. Identify the numerical values of the parameters in whichever of the following forms is appropriate: vc(t) = k₁eat + k₂ ebt + k3 (with |a| < |b|), or vc(t) eat [k₁cos(bt) + k2sin(bt)] + k3. a=160 b = 4950 k₁ V K₂ = V K3 V S-1 S-1