Consider the free vibration responses P, Q, R and S (shown in the figure) of a single
degree of freedom spring-mass-damper system with the same initial conditions. For
the different damping cases listed below, which one of the following options is
correct?
1. Overdamped
2. Underdamped
3. Critically damped
4. Undamped
Options:
(A) P - 1, Q - 4, R - 2, S - 3
(B) P - 1, Q - 2, R - 4, S - 3
(C) P - 3, Q - 4, R - 2, S - 1
(D) P - 3, Q - 2, R - 4, S - 1
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2024 Q.14)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Structural Mechanics** under *Aerospace Structures* (1 Mark, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Structural Mechanics.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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