Use Python and StateMint as your computing tools $.$ Work neatly, and clearly mark your answers. Partial credit may be given.

Consider the linear graph model $($with normal tree$)$ of Fig. $1.$ This is a model of a motor with constant Ka connected to a pair of meshing gears with transformer ratio N$,$ the output over input gear ratio. An ideal voltage source drives the motor$$modeled as an ideal transducer with armature resistance R and inductance L$.$ The motor$$s rotational mechanical side $(2)$ is connected to a moment of inertia J$2$ modeling the rotor and drive gear combined inertia. The damping element B$2$ models the internal motor damping and the drive gear bearing damping. The output side of the gear transducer $(4)$ is connected to a moment of inertia J$4$ modeling the output gear and load combined inertia. The damping element B$4$ models the internal motor damping and the drive gear bearing damping. Use the parameter values given in Table $1.$

a$.)$ Derive a state$-$space model for the system with outputs $$J$2$

and $$J$4.$ b$.)$ Create a Statemint$/$Python ss model for the system and simulate its response from rest to an input voltage VS $=20$ V$.$

c$.)$ Plot the outputs through time until they reach steady state. Please show all work and numbers and variable substitutions respectively. Make your work clear and understandable. Table $1$: System parameter values.$($See attached photo$)$

Figure $1$: A linear graph model with normal tree in green of an electromechanical system with a gear reduction.