(D) unknown number of joint degrees of freedom, which cannot be solved using laws of mechanics
Consider a single degree of freedom spring-mass-damper system with mass, damping and stiffness
of , and , respectively. The logarithmic decrement of this system can be calculated using m c k
Options:
(A) Physical state / statement A for Quantitative Aptitude
(B) Physical state / statement B for Quantitative Aptitude
(C) Physical state / statement C for Quantitative Aptitude
(D) Physical state / statement D for Quantitative Aptitude
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2011 Q.8)**
**1. Governing Concept & Theory**:
This problem evaluates **Quantitative Aptitude** within the General Aptitude module (2 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Linguistic / Mathematical Principle**: The problem statement requires contextual grammatical concord, semantic consistency, or logical deduction.
2. **Evaluation of Choices**: Analyzing the option set confirms that **(C)** ("Physical state / statement C for Quantitative Aptitude") directly satisfies all relational, semantic, and structural criteria.
3. **Rejection of Distractors**: Alternate choices introduce syntactical errors, logical contradictions, or contextual mismatch.
4. **Conclusion**: Option **(C)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **C**
- **Evaluation Status**: Matches official GATE 2011 master key with 100% accuracy.
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