The easiest way to solve any RCL circuit with an input vs(t) is by a difference equation.
Let curr= (q1-q0)/dt
q2=2.*q1-q0 + dt**2*( -q1/(L*c) -(R/L)*curr +vs(t-dt) ).
Then everything else follows ,
Vc(t) = q2/C , VL = L * ( q2-2*q1+q0)/dt^2 , VR = R*(q2-q1)/dt
Give me equations and the solutions ,that is numbers ! if anyone wants to expand or ammend an old theory it must be formulated by means of an equation that improves the old results.