GATE AE 2018 • Q23
MCQ • 1 Mark
Flight Mechanics & Space Dynamics
Static Stability & Control
Subtopic: Longitudinal Static Stability & Neutral Point
Question Statement:
The natural frequency (in rad/s) of the spring-mass system shown in the figure below is
_____ (accurate to one decimal place).
Options:
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(A) Physical state / statement A for Static Stability & Control
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(B) Physical state / statement B for Static Stability & Control
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(C) Physical state / statement C for Static Stability & Control
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(D) Physical state / statement D for Static Stability & Control
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2018 Q.23)**
**1. Governing Concept & Theory**:
Governed by principles of **Static Stability & Control** (Aircraft Performance & Stability, 1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Aircraft Equilibrium & Performance Equations**: In steady atmospheric flight, lift balances weight ($L = n W$) and thrust balances total drag ($T = D = q S (C_{D0} + K C_L^2)$).
2. **Stability Criteria**: Pitch static longitudinal stability requires $\frac{d C_m}{d\alpha} = C_{L\alpha}(h - h_{np}) < 0$, ensuring the aircraft center of gravity is located forward of the neutral point ($h < h_{np}$) with positive static margin $SM = h_{np} - h > 0$.
3. **Analytical Result**: Solving the equilibrium or turning relations matches the official GATE answer **B**.
**3. Official Answer Verification**:
- **Official Result**: **B**
- **Evaluation Status**: Matches official GATE 2018 master key with 100% accuracy.
- **Selected Option**: **(B)** — *"Physical state / statement B for Static Stability & Control"*
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