Consider the RLC circuit with L = 1.0 H, C = 0.40 mF, and R = 100 W. The source is v S(t) = [2 + 8 u(t)] V. d 2 i L(t)/dt 2 + 100 di L(t)/dt + 2500 i L(t) = 0 (see HW #9 Solution Problem 3) Critically Damped s 2 + 100 s + 2500 = 0 gives s 1 = s 2 = - 50 sec -1 (a) Calculate vC(0 + ), i L(0 + ), and v C(+?). (3 pts.) (b) Determine the form of natural solution iLN(t) using the values for s 1 and s 2. (2 pts) (c) Determine the particular solution iLP(t). (1 pt) (d) Determine the complete solution i L(t) for t > 0. (3 pts.) (e) Apply KVL to find an expression for vC(t) in terms of i L(t) and calculate the resulting expression.