$7\mathrm{.}30$ A simple $1-$DOF mechanical system has the following transfer function:

G$($s$)=($Y$($s$))/($U$($s$))=(0\mathrm{.}25)/($s$^(2)+2$s$+9)$

where the position of the mass y$($t$)$ is in meters. The system is initially at rest, y$(0)=$y$^()(0)=0,$ and the

applied force is a step function u$($t$)=4$U$($t$)$N$.$

a$.$ Accurately sketch the system response y$($t$)$ and label all important performance criteria on your sketch.

b$.$ Use MATLAB or Simulink to verify your sketch in part $($a$).$ Plot y$($t$)$ from the numerical solution.

MODEL IN SIMULINK NOT MATLAB PLEASE!!