A uniform bar of mass \(m\) is pivoted at point \(O\) and supported at the ends by two springs, as shown in Fig. 3.59. End \(P\) of spring \(P Q\) is subjected to a sinusoidal displacement, \(x(t)=x_{0} \sin \omega t\). Find the steady-state angular displacement of the bar when \(l=1 \mathrm{~m}\), \(k=1000 \mathrm{~N} / \mathrm{m}, m=10 \mathrm{~kg}, x_{0}=1 \mathrm{~cm}\), and \(\omega=10 \mathrm{rad} / \mathrm{s}\).

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00000 Uniform bar, mass m x(t)=xo sin ot P 00000 31 FIGURE 3.59 Spring subjected to sinusoidal motion.