I am looking for examples of second-order ODE's that are similar to the spring, and pendulum, as well as the LRC, LC, RC, and LR circuits and involve electromagnetism. I know how to solve them, and I am just searching for some in my Physics textbook and didn't find any besides the LRC, and etc. \begin{align}mx''+kx&=0\ \text{spring} \\ L\theta''+g\sin(\theta)&=0 \ \text{pendulum} \\ LQ''+\frac{Q}C&=0 \ \text{Inductor Capacitor} \\ LQ''+RQ'+\frac{Q}C&=0 \ \text{Inductor Resistor Capacitor}\end{align}
Edit
I did try a search its just I found many PDEs instead.