Which of the following statements regarding the longitudinal dynamic modes of an aircraft is/are TRUE?

(A) The Phugoid mode involves significant variations in forward airspeed and altitude at nearly constant angle of attack.

(B) The Short-Period mode involves rapid oscillations in pitch angle and angle of attack at essentially constant forward airspeed.

(C) The damping ratio of the Phugoid mode is typically much lower than that of the Short-Period mode.

(D) The Phugoid mode has a much higher oscillation frequency than the Short-Period mode.

Answer Key:

A,B,C

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Modal Decoupling:** Small perturbation analysis splits longitudinal dynamics into short-period and phugoid modes. 2. **Stage 2: Phugoid Characteristics:** Frequency $\omega_{np} \approx \sqrt{2} \frac{g}{V}$, very low frequency, low damping (statement A and C TRUE; statement D FALSE). 3. **Stage 3: Short Period Characteristics:** Frequency $\omega_{nsp}$ is high, heavily damped, constant speed (statement B TRUE). 4. **Stage 4: Correct Answers:** A, B, and C.

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