Two$-$degrees$-$of$-$freedom approximation for short period approximation is given below$\mathrm{.}28,$IN$=+$MaZaMa $+$Ma$,+$ The stability characteristics data for a general aviation airplane flying at $176$ ft$/$s and sea level aregiven asZa $=-355$ ft$/$s$\text{'}$ M$.=-0\mathrm{.}9/$s $++$ M$.=-8\mathrm{.}8/$s$\text{'}+$ M$,=-2\mathrm{.}05/$s$($a$)-$Find the characteristic equation of the short period mode.$($b$)-$Calculate the natural frequency, the damping ratio, and the poles of the short period mode.