GATE_AE_2027_MOCK_05_Q63 GATE 2027 Aerospace Engineering All-India Master Mock 05 (High-Yield Comprehensive Grand Finale) NAT · 2 Marks
Aerospace Structures • Structural Dynamics & Aeroelasticity • Single & Multi-DOF Vibration Systems

An aircraft engine pylon is modeled as a spring-mass system with mass m = 500 kg and natural frequency f_n = 10 Hz. What is the equivalent stiffness k of the pylon in kilonewtons per meter (kN/m)? (Take pi^2 ≈ 9.8696, round to nearest integer).

Answer Key:
1974

Step-by-Step Verified Solution

### Solution: \omega_n = 2\pi f_n = 2 * 3.1416 * 10 = 62.832 rad/s. k = m * \omega_n^2 = 500 * (62.832)^2 = 500 * 3947.84 = 1973920 N/m ≈ 1974 kN/m. Correct: 1974 (range 1965 to 1985).
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