Problem $7$

The modeling equations of a system are given below. The overall system input and output variables are $u$

and $y,$ respectively.

$2z^{}+z=u$

$y^{}+6y=4z$

$($a$)$ Sketch the simplest possible block diagram for the case where all variables have zero initial

conditions. Label all blocks and signal path variables.

$($b$)$ Sketch the block diagram for the case where the initial conditions are : $z(0)=2$ and $y(0)=-3.$

Label all blocks and signal path variables.