\(\frac{q}{c}-i R-I \cdot \frac{d i}{d t}=0\)

\(\mathrm{i}=-\frac{\mathrm{d} q}{\mathrm{dt}} \Rightarrow \frac{\mathrm{q}}{\mathrm{c}}+\frac{\mathrm{dq}}{\mathrm{dt}} \mathrm{R}+\frac{\mathrm{Ld}^{2} \mathrm{q}}{\mathrm{dt}^{2}}=0\)

\(\frac{d^{2} q}{d t^{2}}+\frac{R}{I} \frac{d q}{d t}+\frac{q}{I c}=0\)

From damped harmonic oscillator, the amplitude is given by \(\mathrm{A}=\mathrm{A}_{0} \mathrm{e}-\frac{\mathrm{dt}}{2 \mathrm{m}}\)

Double differential equation \(\frac{\mathrm{d}^{2} \mathrm{x}}{\mathrm{dt}^{2}}+\frac{\mathrm{b}}{\mathrm{m}} \frac{\mathrm{dx}}{\mathrm{dt}}+\frac{\mathrm{k}}{\mathrm{m}} \mathrm{x}=0\)

\(\mathrm{Q}_{\max }=\mathrm{Q}_{\mathrm{o}} \mathrm{e}-\frac{\mathrm{Rt}}{2 \mathrm{L}} \Rightarrow \mathrm{Q}_{\max }^{2}=\mathrm{Q}_{\mathrm{o}}^{2} \mathrm{e}-\frac{\mathrm{Rt}}{\mathrm{L}}\)

Hence damping will be faster for lesser self inductance