Problem $7(7$ pts$.)$: The transfer function of a certain system is given by

$()=()$

$(++)(++)$

where N$($s$)$ is an unspecified numerator polynomial.

Assume the input to this system is $()=().$

Using arbitrary notations for the constant coefficients and phases, write the general form of the

response Y$($s$),$ and of the corresponding time domain $().$ Identify the natural and forced

components of the response.

$($Assume that no roots of N$($s$)$ are the same as poles of either G$($s$)$ and X$($s$)).$