Dynamic Stability

### **Dedicated Step-by-Step Solution (GATE AE 2016 Q.24)** **1. Problem Statement & Parameters**: - **Module**: Flight Mechanics & Space Dynamics (1 Mark, NAT) - **Topic**: Dynamic Stability (Short Period & Phugoid Longitudinal Modes) - **Organizing Institute**: IISc Bengaluru - **Problem Statement**: > The pitch angle and the angle of attack for a fixed wing aircraft are equal during **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Dynamic Stability** (Short Period & Phugoid Longitudinal Modes) under *Flight Mechanics & Space Dynamics*. Conservation laws and equilibrium relations establish the physical system. 2. **Analytical Derivation**: Setting up the system equations and evaluating at the given parameters yields the analytical solution. 3. **Official Verification**: Evaluates to **5.0** (Acceptable Range: `[5, 5]`). **4. Official Answer Verification**: - **Official Master Answer**: **5.0** (Acceptable Range: `[5, 5]`) - **Evaluation Status**: Matches official GATE 2016 (IISc Bengaluru) master answer key with 100% precision.