For the rotational system shown in the figure below do the following:

D$\_(1)=1$N$-$m$-($s$)/($r$)$ad$,$D$\_(2)=2$N$-$m$-($s$)/($r$)$ad

N$\_(1)=2,$N$\_(2)=4,$N$\_(3)=8,$N$\_(4)=16$

K$\_(1)=2$N$-($m$)/($r$)$ad

J$\_(1)=1$kg$-$m$^(2),$J$\_(2)=4$kg$-$m$^(2)\backslash$theta $\_(2)($s$)$ lineT$($s$).$ Hint: find projected K$\_(1),$D$\_(1),$J$\_(1),\backslash$theta $\_(1)($s$),$T$($s$)(2$pts$)$

$($b$)$ Find the transfer function, G$($s$)=\backslash$theta $\_(2)($s$)/($T$)($s$).(2$ pts$)$

$($c$)$ Write the state space equations in vector$-$matrix form, including the output equation. Assume that the output is measured at $\backslash$theta $\_(2)($t$).(1$ pts $)$