Considering the dynamic system below:

a$)$ List the elements in the system. Then, categorize them into inertia, spring, damper, and source elements. How many ODEs do you need to model this system? Why? $(2$ 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. $(8$ points$)$

d$)$ Use KVL$,$ KCL$,$ and Ohm law to redefine the not$-$good terms. $(8$ points$)$a$)$ List the elements in the system. Then, categorize them into inertia, spring, and damper elements.

$(2$ points$)$

b$)$ How many differential equations do you need to model this system? Why? $(2$ points$)$

c$)$ Consider the coordinate systems shown, assume $1>2>3$ and $1>2>3,$ isolate $1$ and

$2,3$ and derive the FBD$.(8$ points$)$

d$)$ Based on your FBD$,$ use the EoM and find the model for the system. $(8$ points$)$