For what range of frequency ratios \(\omega / \omega_{n}\) will the magnification factor \(\beta\) be greater than 1 for the idealized model of Figure 3.58? For what range of frequency ratios will the magnification factor be greater than \(86 \%\) of the peak response? Let \(m=\) 1 slug, \(k=9 \mathrm{lb} / \mathrm{in}\), and \(\zeta=0.15\). Show the cases on a plot of the magnification factor vs. frequency ratio.

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eelle W F(t) = A sin cox Tx(1) Figure 3.58: Harmonically driven oscillator.