GATE AE 2008 • Q56 MCQ • 2 Marks Aerospace Structures

Aerospace Structures

Structural Dynamics & Aeroelasticity

Subtopic: Free & Forced Vibrations of Continuous Beams

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

Official Answer Key:

A

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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