Here is just the case when the exact solution is worse than numerical. Therefore, we solve numerically
Manipulate[
Plot[Evaluate[
y[t] /. First[
NDSolve[{L*y''[t] == -R*y'[t] - C0*y[t] + V*Sin[t], y[0] == 0,
y'[0] == V}, y, {t, 0, 2*Pi}]]], {t, 0, 2*Pi}], {{L, 1*^-3},
10^-6, 10*^-3}, {{R, 3*^3}, 1*^3, 10*^3}, {{C0, 3*^5}, 0,
10*^5}, {{V, 5}, 0, 10}]
