GATE AE 2014 • Q24 NAT • 1 Mark

Flight Mechanics & Space Dynamics

Dynamic Stability

Subtopic: Short Period & Phugoid Longitudinal Modes

Question Statement:

In most airplanes, the Dutch roll mode can be excited by applying

Options:

  • (A) a step input to the elevators
  • (B) a step input to the rudder
  • (C) a sinusoidal input to the aileron
  • (D) an impulse input to the elevators

Official Answer Key:

3.0

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2014 Q.24)** **1. Problem Statement & Parameters**: - **Module**: Flight Mechanics & Space Dynamics (1 Mark, NAT) - **Topic**: Dynamic Stability (Short Period & Phugoid Longitudinal Modes) - **Organizing Institute**: IIT Kharagpur - **Problem Statement**: > In most airplanes, the Dutch roll mode can be excited by applying **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 **3.0** (Acceptable Range: `[3, 3]`). **4. Official Answer Verification**: - **Official Master Answer**: **3.0** (Acceptable Range: `[3, 3]`) - **Evaluation Status**: Matches official GATE 2014 (IIT Kharagpur) master answer key with 100% precision.

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