In typical conventional aircraft, longitudinal flight model linearization results in transfer functions with two pairs of complex conjugate poles. Consequently, the natural response for these airplanes has two modes in their natural response. The "short period" mode is relatively well-damped and has a high-frequency oscillation. The "phugoid mode" is lightly damped and its oscillation frequency is relatively low. For example, in a specific aircraft the transfer function from wing elevator deflection to nose angle (angle of attack) is (McRuer, 1973):

Theta(s)/Zeta(s) = 30(s+0.003)(s+10)/(s2+5.6s+23.05)(s 2+0.0122s+0.00011642)

(a). Find which of the poles correspond to the short period mode:
(b). Find which of the poles correspond to the phugoid mode.