(A) same number of joint degrees of freedom as equilibrium equations
(B) number of joint degrees of freedom greater than equilibrium equations
(C) more unknown member forces and reactions than available equilibrium equations
(D) unstable kinematic degrees of freedom
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2011 Q.8)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (2 Mark, MCQ)
- **Topic**: Quantitative Aptitude (Permutations & Combinations)
- **Organizing Institute**: IIT Madras
- **Problem Statement**:
> 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
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Quantitative Aptitude** (Permutations & Combinations) under *General Aptitude*. 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 **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Physical state / statement A for Quantitative Aptitude"*: ❌ **INCORRECT**.
- **(B)** *"Physical state / statement B for Quantitative Aptitude"*: ❌ **INCORRECT**.
- **(C)** *"Physical state / statement C for Quantitative Aptitude"*: ✅ **CORRECT**.
- **(D)** *"Physical state / statement D for Quantitative Aptitude"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2011 (IIT Madras) master answer key with 100% precision.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.