Problem 2 (50%): Longitudinal Dynamic Stability Analysis The following problem aims to study aircraft dynamic stability for successfully achieving various missions. The stability and control derivatives at SL are given as follow: (X = -0.1125/s Xu Xw = 0.09 ft/s Zu = -0.9225/s Zw=-5.05 ft/s (Zse = -19.8 ft/s M8 = -5.27 1/s Z = 440 ft/s Za M = 0.0047/s Mw = -0.099/s M = -7.37/s Ma S = 184 ft, b = 33.4 ft, c 5.7 ft, and m = 2750 lb. Q1: Build the state-space model that corresponds to the longitudinal motion (x [Au Aw Aq A0], u = 8e). Q2: In general, an airplane longitudinal motion is characterized by two motion modes: one and one slow: Find and plot the airplane eigenvalues in the complex plane and explain their sta degree. Find the eigenvalues of each mode (i.e., fast, and slow modes). Find the frequency and damping ratio for each mode. Compare the two modes in terms of frequency, period, and time of half amplitude. Q3: Find the airspeed t uo