LRC series circuit

Question

Find the charge on the capacitor in an LRC series circuit when L = 0.5 h, R = 10 Ω, C = 0.01 f, E(t) = 150 V, q(0) = 1 C and i (0) = 0 A. What is the charge on the capacitor after a long time?

Answer 1

this is a 2nd order diff eq.

the complete solution including complimentary and particular is:

q= e^-10t _{(c1 cos 10t+ c2 sin 10t) +(3/40)}

_{as t becomes large, i.e. approaches infinity,}

_{q(large time) = (3/40) C}