Natural frequency of an undamped operator seat is 5 Hz, and combined weight of the seat and the operator is 880 N. If there are four springs fitted in parallel below the operator seat, the spring rate (or stiffness) of each spring in kN m⁻¹ is ______
Official Answer Key:
21 to 23
Step-by-Step Solution & Explanation
For an undamped single-DOF system, ωₙ = √(k_total/m), so k_total = m×(2πf)². Mass m = W/g = 880/9.81 = 89.7 kg. k_total = 89.7×(2π×5)² = 89.7×987.0 = 88,535 N/m. With 4 identical springs in parallel, k_each = k_total/4 = 88,535/4 = 22,134 N/m ≈ 22.1 kN/m, within the accepted band 21–23.
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