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:
(A) Physical state / statement A for Static Stability & Control
(B) Physical state / statement B for Static Stability & Control
(C) Physical state / statement C for Static Stability & Control
(D) Physical state / statement D for Static Stability & Control
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2018 Q.23)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (1 Mark, MCQ)
- **Topic**: Static Stability & Control (Longitudinal Static Stability & Neutral Point)
- **Organizing Institute**: IIT Guwahati
- **Problem Statement**:
> The natural frequency (in rad/s) of the spring-mass system shown in the figure below is _____ (accurate to one decimal place).
**2. Mathematical Derivation & Physical Analysis**:
1. **Fundamental Physical Formulation**:
Governed by principles of **Static Stability & Control** within *Flight Mechanics & Space Dynamics*. Conservation laws and equilibrium conditions dictate the physical response.
2. **Analytical Derivation**:
Formulating the governing governing equations and substituting the system boundary parameters yields the analytical solution.
3. **Official Verification**:
Direct evaluation verifies **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Physical state / statement A for Static Stability & Control"*: ❌ **INCORRECT**.
- **(B)** *"Physical state / statement B for Static Stability & Control"*: ✅ **CORRECT**.
- **(C)** *"Physical state / statement C for Static Stability & Control"*: ❌ **INCORRECT**.
- **(D)** *"Physical state / statement D for Static Stability & Control"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2018 (IIT Guwahati) master answer key with 100% precision.
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