Unlike RC and RL circuits, solving RLC circuits involves second order differential
equations which can produce under-damped, over-damped, or critically damped
responses. Simple KCL and KVL equations can be used to derive these second
order differential equations. The solution of the characteristic equation (of the
second order differential equation) yields the form of the response. Finally, the
initial conditions on the inductor or capacitor yield the equations necessary to
solve for the coefficients in the solution.