An uniform rigid bar of length (ell=50 mathrm{~cm}) and mass (m=7 mathrm{~kg}) is hinged at one end

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An uniform rigid bar of length \(\ell=50 \mathrm{~cm}\) and mass \(m=7 \mathrm{~kg}\) is hinged at one end (Figure P1.7). At the other end, this bar is suddenly attached to a massless spring with stiffness \(k=1,000 \mathrm{~N} / \mathrm{m}\). Derive an expression for the angular oscillation of the bar.

Figure P1.7

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