For the case where the source is an unchanging voltage, the second order differential equation governing the current in the LCR circuit is :
For the RLC circuit, there are two important parameters,
is the natural frequency of the circuit.
A useful parameter is the damping factor, ζ which is defined as the ratio of these two,
The general solution of the differential equation is an exponential in either root or a linear superposition of both,
Based on above one gets different condition of oscillatory response, via., underdamped, overdamped and critically damped.
For more details see