$$\begin{aligned}
   \label{Ide} 
I'' + \left( \frac{R}{L} + \frac{C'}{C} \right) I' + \left( \frac{1 + R C'  + R' C}{LC} \right) I  = 0. \end{aligned}$$ Similarly, the voltage $V(t)$ across the capacitance $C(t)$ evolves according to $$\begin{aligned}
   \label{Vde} 
V'' + \left( \frac{R}{L} + \frac{2 C'}{C} \right) V' + \left( \frac{1 + R C' + L C''}{LC} \right) V = 0, \end{aligned}$$ which follows from (\[RLC\_Q\]) using $Q = CV$ and assuming $C(t) \neq 0$.

To determine the circuit parameters from measurements of the current $I(t)$ or voltage $V(t)$, the differential equation was approximately reconstructed by fitting the data with the trial function $$\begin{aligned}
   \label{trialfn} 
y(t) = A_0 e^{- B(t)} \cos[D(t) + \phi_0], \end{aligned}$$ where the fit parameters $A_0$ and $\phi_0$ are constant but the functions $B(t)$ and $D(t)$ depend on time. This form assumes the burst start time is known, and that there is no background offset (which was removed by fitting with an offset parameter). This trial function satisfies the differential equation $$\begin{aligned}
   \label{recoveredDE}
y'' + U(t) \, y' + W(t) \, y  = 0\end{aligned}$$ where the functions $U(t)$ and $W(t)$ may be computed as $$\begin{aligned}
   \label{Ut}
U(t) &= 2 B' - {D''}/{D'}   \\
W(t) &= \left( B' \right)^2 + 