Problem$5.(15$ points$)$

$($a$)$ Obtain the transfer functions $x\frac{s}{F}(s)$ and $Y\frac{s}{F}(s)$ for the following model

$x^{}=-6x+3y+f(t),y^{}=-9y-8x+g(t)$

$($b$)$ Compute $,,{}_n$ and ${}_d$ for the model.

$($c$)$ If $f(t)=g(t)=0,$ estimate how long it take for the responses $x(t)$ and $y(t)$ to disappear.