$3\mathrm{.}5$ A load inertia $I_5$ is driven through a double gear pair by a motor with inertia $I_4($Figure P$3\mathrm{.}5)7_4)$ shaft inertias are negligible. The gear inertias are $f_1,l_2,$ and $l_3.$ The speed ratios are given fats figure. The motor torque is $T_1,$ and the viscous damping coefficient is $c=5\mathrm{.}4N*m*\frac{s}{r}ad.$ Neglet elasticity in the system, and use the following inertia values $($in $kg*m^2)$:

$I_1=0\mathrm{.}136,I_2=0\mathrm{.}272$

$I_1=0\mathrm{.}544,I_4=0\mathrm{.}408$

$I_5=0\mathrm{.}952$

FIGURE P$3\mathrm{.}5$

$3\mathrm{.}5$ A load inertia $I_5$ is driven through a double gear pair by a motor with inertia $I_4($Figure P$3\mathrm{.}511.$y shaft inertias are negligible. The gear Inertias are $f_1,f_2,$ and $f_3.$ The speed ratios are given figure. The motor torque is $T_1,$ and the viscous damping coefficient is $c=5\mathrm{.}4N-$m$-$s$/$rad$.$ Nefes elasticity in the system, and use the following inertia values $($in $kg*m^2)$:

$I_1=0\mathrm{.}136,I_2=0\mathrm{.}272$

$I_3=0\mathrm{.}544,I_4=0\mathrm{.}408$

$I_5=0\mathrm{.}952,$

FGURE P$35$

Derive the model for the motor shaft speed of with $71$ a given function of time.