Old spec 3.4 example, third order system with poles on the imaginary axis (ENGR5001)

Old spec 3.4 example, third order system with poles on the imaginary axisTutorialOld spec ENGR2022:26 min

Find the poles and zeros of the system below and determine its stability. Which poles dominate? $X = \frac{5}{s^3 + s^2 + 5s + 5}U$

Formulas you may need

Poles on the imaginary axis (non-repeated), the rest in the left half plane: marginally stable (learn this)

real pole =

imaginary part of complex poles (+) =