For a series RLC circuit, the differential equation is
If v_{T}(t) is a constant or zero ( v_{T}(t) = V_{T}), and the system has initial conditions , and , then the solution to this equation is
(R_{T} C)^{2}  4LC > 0  (R_{T} C)^{2}  4LC = 0  (R_{T} C)^{2}  4LC < 0 
Overdamped  Critically Damped  Underdamped 



K_{1} = V_{o}  V_{T}  K_{1} = V_{o}  V_{T} 

For a parallel RLC circuit, the differential equation is
If i_{N}(t) is a constant or zero ( i_{N}(t) = I_{N}), and the system has initial conditions , and , then the solution to this equation is
(G_{N} L)^{2}  4LC > 0  (G_{N} L)^{2}  4LC = 0  (G_{N} L)^{2}  4LC < 0 
Overdamped  Critically Damped  Underdamped 



K_{1} = I_{o}  I_{N}  K_{1} = I_{o}  I_{N} 
