Use the method of renormalization to determine a two-term approximation for the frequency-amplitude relation for the system of Figure P12.4. If the bar is rotated \(4{ }^{\circ}\) from equilibrium and released, what is the period for \(L=4 \mathrm{~m}\), \(k=1000 \mathrm{~N} / \mathrm{m}\), and \(m=10 \mathrm{~kg}\) ?

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|- L/4 3L/4 FIGURE P12.4 Slender rod of mass m 77777