Question 3: A Boeing 747-400 initially in straight, level flight at 10,000 ft with airspeed 650 ft/sec has the following transfer function relating elevator deflection (input, in deg) to climb rate response (output, in ft/min) G(s) 90(60s+30s - 0.3) 78488311s2 +0.2s + 0.2 (you'll learn how to derive such transfer functions in ENAE403!) a.) Identify the poles and zeros of this transfer function. Rewrite G(s) in the ZPK form; use the second-order convention as appropriate. b.) Is the aircraft stable? Why, or why not? c.) There are two second-order modes in the dynamics: a slowly decaying oscillation conventionally called the "phugoid mode", and a more rapidly decaying oscillation called the "short period mode. Identify the oscillation frequency and damping ratio of each mode. d.) Suppose the pilot desires the aircraft to exhibit a constant steady-state climb rate of 1000 ft/min. What constant elevator deflection would be required to achieve this? e.) After the elevator is deflected as in d.), estimate how long it would take the natural dynamics of the aircraft to settle to within 2% of the desired steady-state climb rate. f.) Show that there exists a monotonically increasing elevator input of the form eat with real a > 0 such that the steady-state climb rate will actually be zero. Identify the required numerical value of a. g.) Determine the exact differential equation which models the climb rate response of the aircraft due to elevator inputs. Assume variables u(t) and y(t) have their indicated units (no conversions are needed).