Problem #$8$: $(50$ points$)$ A second$-$order system has the following differential equation:

$53$Yees $+45$ VEs$)+4$ Tess $=2/5$

dy$($t$)$

dt$?$

$14$

dy $($E$)+47(+)=2$u$($t$)$

Where u$($t$)$ is the input and y$($t$)$ is the output.

A$.$ Find the transfer function H$($s$)$ of the system.

$2$

$/$s$)=$

$52+4$s$+4$

$1$

$(15$ points$)[$

$(10$ points$)$ Provide the key formula and the solution procedures.

B$.$ Calculate the step response of the system. $($Hint: a step input U$($s$)=2/$s$)$

$(15$ points$)|$ Y$($S$)=$

$-26$

$(10$ points$)$ Provide the key formula and the solution procedures.