Question Statement:
A linear mass-spring-dashpot system is over-damped. In free vibration, this system undergoes
Options:
-
(A) non-oscillatory motion
-
(B) random motion
-
(C) oscillatory and periodic motion
-
(D) oscillatory and non-periodic motion
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2015 Q.10)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (2 Mark, MCQ)
- **Topic**: Analytical & Spatial Aptitude (Analogy & Shape Transformation)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> A linear mass-spring-dashpot system is over-damped. In free vibration, this system undergoes
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Analytical & Spatial Aptitude** (Analogy & Shape Transformation) 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)** *"non-oscillatory motion"*: ❌ **INCORRECT**.
- **(B)** *"random motion"*: ❌ **INCORRECT**.
- **(C)** *"oscillatory and periodic motion"*: ✅ **CORRECT**.
- **(D)** *"oscillatory and non-periodic motion"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2015 (IIT Kanpur) master answer key with 100% precision.
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