Chapter 3, Problem 3.23P

For the geared system shown in Figure P3.23, assume that shaft inertias and the gear inertias $I_1$ , $I_2$ , and $I_3$ are negligible. The motor and load inertias in $\text{kg}\cdot {\text{m}}^2$ are

$I_4=0.03I_5=0.15$

Figure P3.23

The speed ratios are

$\frac{{\omega }_1}{{\omega }_2}=\frac{{\omega }_2}{{\omega }_3}=1.6$

Derive the system model in terms of the speed ${\omega }_3$ , with the applied torque T as the input.