Problem $5(20$ pts$)$ Derive from scratch using paper and pencil $($or in a tablet$)$ the dynamic model of the electromagnet of Fig. $1($on the next page$)$ where it is considered that $f_e$ is directed from right to left. In other words, conduct similar derivation steps as we did in class from slide $13$ to $25.$ Recall that the dynamic model must be expressed as an ordinary differential equation. How many states does your model have? Please, name those states.