To determine the equivalent moment of inertia of a rigid helicopter component, an engineer decides to run a test in which she pins the component a distance of \(40 \mathrm{~cm}\) and mounts the component on two springs of stiffness \(3.6 \times 10^{5} \mathrm{~N} / \mathrm{m}\), as shown in Figure P4.8. She then provide a harmonic excitation to the component at different frequencies and finds that the maximum amplitude occurs at \(50 \mathrm{rad} / \mathrm{s}\). What is the equivalent centroidal moment of inertia predicted by the test?

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3.6 105 N/m 40 cm 10cm G Mo sin at 3.6 105 N/m Helicopter component FIGURE P4.8 m = 4 Kg