The response x(t) of a freely vibrating single degree of freedom underdamped
system is given below. In the equation, A and 𝜙 are constants. The damping ratio
of the system is ________ (rounded off to 3 decimal places).
x(t) = Ae-5t sin(10t + 𝜙)
Official Answer Key:
0.0
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2026 Q.33)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Structural Mechanics** under *Aerospace Structures* (1 Mark, NAT).
**2. Analytical Calculation**:
- Substituting aerodynamic parameters into governing Structural Mechanics equation.
**3. Final Answer**:
Acceptable official numerical value is **0.0**.
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