Question Statement:
What will be the logarithmic decrement if a free vibration test is performed?
Options:
-
(A) /40
-
(B) 7/20
-
(C) 7/10
-
(D) 7/5
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.56)**
**1. Problem Statement & Parameters**:
- **Module**: Propulsion (2 Mark, MCQ)
- **Topic**: Compressors and Turbines (Centrifugal Compressors)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> What will be the logarithmic decrement if a free vibration test is performed?
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Compressors and Turbines** (Centrifugal Compressors) under *Propulsion*. 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 **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"/40"*: ✅ **CORRECT**.
- **(B)** *"7/20"*: ❌ **INCORRECT**.
- **(C)** *"7/10"*: ❌ **INCORRECT**.
- **(D)** *"7/5"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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