Question: ( 1 0 pts ) Given the servomotor and load shown in the figure below, and assuming the motor and gears have negligible inertia, show

(10

pts

)

Given the servomotor and load shown in the figure below, and assuming the motor and gears have negligible inertia, show that the system is governed by the following coupled differential equations:

J_{L}_{L}^{} (t) + B_{L}_{L}^{} (t) = k_{t} \frac{N_{2}}{N_{1}} i_{a} (t)

L_{a} \frac{d}{d t} i_{a} (t) + R_{a} i_{a} (t) + k_{b} \frac{N_{2}}{N_{1}}_{L}^{} (t) = V_{a} (t)

( 1 0 pts ) Given the servomotor and load shown

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