Consider the following transfer function:

$Gs=\frac{\text{n}\text{u}\text{m}s}{\text{d}\text{e}\text{n}s}=\frac{5s+2}{s^2+8s+52}$

Use the method of completing the square to find $gt=L^{-1}Gs.$

Write the partial fraction of $Gs$ and then find $gt=L^{-1}Gs$ by using complex

algebra.

Find the residues of $Gs$ by hand calculations.

Use the symbolic MATLAB command ilaplace $($See help ilaplace$)$ to find

$gt=L^{-1}Gs$ and compare your finding with $(5).$