GATE_AE_2027_MOCK_04_Q63 GATE 2027 Aerospace Engineering All-India Master Mock 04 (Aerospace Structures, Thin-Walled Beams & Aeroelasticity) NAT · 2 Marks
Aerospace Structures • Structural Dynamics & Aeroelasticity • Single & Multi-DOF Vibration Systems

A single-degree-of-freedom spring-mass system has mass m = 4.0 kg and undamped natural frequency \omega_n = 50 rad/s. What is the spring stiffness k in N/m?

Answer Key:
10000

Step-by-Step Verified Solution

### Solution: \omega_n = sqrt(k / m) ==> k = m * \omega_n^2 = 4.0 * (50)^2 = 4.0 * 2500 = 10000 N/m. Correct: 10000.
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