Consider the gear system given below. Create a system dynamics model representing the motion of the system. For $i=1,2,3,$ gear i has $N_i$ teeth, radius $r_i,$ diameter $d_i,$ moment of inertia $I_i,$ rotational angle ${}_i,$ and rotational angular velocity ${}_i.$ In creating the system model, draw three free body diagrams. Determine the transfer function from input torque $T$ to output shaft angular velocity ${}_3.$

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