GATE AE 2023 • Q25 MSQ • 1 Mark

Aerospace Structures

Structural Mechanics

Subtopic: Thin-Walled Shells & Buckling

Question Statement:

Which of the following statement(s) is/are true about harmonically excited forced vibration of a single degree-of-freedom linear spring-mass-damper system?

Options:

  • (A) The total response of the mass is a combination of free vibration transient and steady-state response.
  • (B) The free vibration transient dies out with time for each of the three possible conditions of damping (under-damped, critically damped, and over-damped).
  • (C) The steady-state periodic response is dependent on the initial conditions at the time of application of external forcing.
  • (D) The rate of decay of free vibration transient response depends on the mass, spring stiffness and damping constant.

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE AE 2023 Q.25)** **1. Governing Concept & Syllabus Domain**: This question pertains to **Structural Mechanics** under *Aerospace Structures* (1 Mark, MSQ). **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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