GATE_AE_2027_MOCK_03_Q63 GATE 2027 Aerospace Engineering All-India Master Mock 03 (Flight Dynamics, Controls & Space Trajectories) NAT · 2 Marks
Aerospace Structures • Structural Dynamics & Aeroelasticity • Single & Multi-DOF Vibration Systems

A single-degree-of-freedom aircraft instrument mount has mass m = 2.0 kg and spring stiffness k = 1800 N/m. The viscous damping coefficient is c = 12 N*s/m. What is the damping ratio \zeta of the system?

Answer Key:
0.10

Step-by-Step Verified Solution

### Solution: Critical damping c_c = 2 * sqrt(k * m) = 2 * sqrt(1800 * 2) = 2 * sqrt(3600) = 2 * 60 = 120 N*s/m. Damping ratio \zeta = c / c_c = 12 / 120 = 0.10. Correct: 0.10.
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