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 Matlab 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.Table $1$: System parameter values.

Figure $1$: A linear graph model with normal tree in green of an electromechanical

system with a gear reduction.