Problem $2(12$ points$)$

Convert the electrical circuits shown in $(1)$ and $(2)$ below into a linear mechanical

equivalent. Derive the equations of motion for both the electrical and mechanical systems

including only the input and output variables indicated in the diagram, and identify which

conditions between the parameters of the electrical and mechanical systems are

necessary to make the two systems equivalent $($i$.$e$.$ their equations of motion are the

same$).$