Problem $5,20$ pt

For the following system

$H(s)=\frac{2s+1}{s^2+2s+5}$

$(1)$ It is a second order system, what is the damping ratio? What is the natural frequency?

$(2)$ Solve the step response $y(t)$

$(3)$ By looking at the solution you obtained, draw the curve of the solution $y(t).$ Explain the

rationale you used or the guidelines you used to draw the curve

$(4)$ Plot the curve use any computer software you know and compare it with your hand$-$

drawing.