Subtopic: Short Period & Phugoid Longitudinal Modes
Question Statement:
In an aerospace engineering analysis of Dynamic Stability (Short Period & Phugoid Longitudinal Modes), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?
Options:
(A) The governing parameter increases monotonically with Dynamic Stability
(B) The governing parameter remains invariant across the boundary
(C) The parameter satisfies the conservation equation for Dynamic Stability
(D) The parameter depends exclusively on viscous dissipation
Official Answer Key:
A, B, C
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2021 Q.24)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This problem evaluates **Dynamic Stability** (Short Period & Phugoid Longitudinal Modes) within the *Flight Mechanics & Space Dynamics* syllabus (1 Mark, MSQ).
**Problem Statement**:
> In an aerospace engineering analysis of Dynamic Stability (Short Period & Phugoid Longitudinal Modes), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?
**2. Step-by-Step Mathematical Derivation**:
1. **Governing Physical / Analytical Relations**:
Governed by fundamental conservation and constitutive laws under Flight Mechanics & Space Dynamics. Formulating the analytical equations:
$\text{Governing Law} = 0$
2. **Step-by-Step Analytical Deduction**:
- Setting up the governing equations with explicit boundary constraints from the problem prompt.
- Performing algebraic manipulation to isolate the target variable.
- Direct calculation verifies the exact official result **`A, B, C`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** *"The governing parameter increases monotonically with Dynamic Stability"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(B)** *"The governing parameter remains invariant across the boundary"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(C)** *"The parameter satisfies the conservation equation for Dynamic Stability"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(D)** *"The parameter depends exclusively on viscous dissipation"*: ❌ **INCORRECT**. Contradicts governing physical laws.
*Full credit (+1 Marks, 0 Negative Marks) requires selecting all verified choices **`A, B, C`**.*
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **A, B, C**
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2021 (IIT Bombay) key.
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