A comparison is drawn between damped oscillator and LCR series circuit when an AC voltage is applied on it. The equivalent of damping constant in LCR circuit is

In a series LCR circuit variation of charge i=on capacitor equation is given by 

$$\begin{gathered} \frac{{\mathrm{d}}^2\mathrm{q}}{{\mathrm{dt}}^2}+\frac{\mathrm{R}}{\mathrm{L}}\frac{\mathrm{dq}}{\mathrm{dt}}+\left(\frac{1}{\mathrm{LC}}\right)\mathrm{q}= \frac{\mathrm{V}}{\mathrm{L}} \\ \mathrm{if} \mathrm{you} \mathrm{compare} \mathrm{this} \mathrm{with} \mathrm{the} \mathrm{spring} \mathrm{mass} \mathrm{damped} \mathrm{oscillator} \\ \frac{{\mathrm{d}}^2\mathrm{x}}{{\mathrm{dt}}^2}+\frac{\mathrm{b}}{\mathrm{m}}\frac{\mathrm{dx}}{\mathrm{dt}}+\left(\frac{\mathrm{k}}{\mathrm{m}}\right)\mathrm{x}= 0 , \mathrm{where} \mathrm{b} \mathrm{is} \mathrm{the} \mathrm{damping} \mathrm{constant} , \mathrm{then} \mathrm{R} \mathrm{is} \mathrm{the} \mathrm{equivalent} \mathrm{damping} \mathrm{constant} \mathrm{in} \mathrm{the} \mathrm{LCR} \mathrm{oscillation} \mathrm{equation} . \end{gathered}$$