Considering the dynamic system below:

a$)$ List the elements in the system. Then, eategorize them into inertia, spring, damper, and source elements. How many ODEs do you need to model this system? Why? $(3$ points$)$

b$)$ Identify the dynamic variables in your system $(2$ points$)$

c$)$ Write the ODEs for the energy$-$storing elements. Label the terms as good and not good. $(5$ points$)$

d$)$ Use KVL$,$ KCL$,$ and Ohm law to redefine the not$-$good terms. $(10$ points$)$