### LCR circuit

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,

and

is the natural frequency of the circuit.

A useful parameter is the damping factor, ΞΆ 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,

where,

Based on above one gets different condition of oscillatory response, via., underdamped, overdamped and critically damped.

*For more details see*

http://en.wikipedia.org/wiki/RLC_circuit