For the following transfer function,

$\frac{Y(s)}{x(s)}=\frac{8(s^2+s)}{(s^2+2s+2)(s+2)}$

$($a$)$ Plot the poles and zeros on the complex plane

$($b$)$ Ignoring the zeros, i$.$e$.,$

$\frac{Y(s)}{x(s)}=\frac{8}{(s^2+2s+2)(s+2)}$

If $x(s)$ represents a unit$-$step function, qualitatively sketch and explain the expected

time response $y(t)?$

$($c$)$ What is the steady$-$state gain?

$($d$)$ For the following function,

$\frac{Y(s)}{x(s)}=\frac{8}{(s^2+2)(s+2)}$

If X$($s$)$ represents a unit$-$step function, explain how each "term" in the transfer function

may contribute to the expected time response $y(t).$