Find the undamped natural frequencies of longitudinal vibration of the stepped bar shown in Fig. 12.39 with the following data using consistent- and lumped-mass matrices: \(l_{1}=l_{2}=l_{3}=0.2 \mathrm{~m}, \quad A_{1}=2 A_{2}=4 A_{3}=0.4 \times 10^{-3} \mathrm{~m}^{2}, E=2.1 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\), and \(ho=7.8 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\).

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A A2 14 x, X A3 12 13 FIGURE 12.39 Fixed-fixed three-stepped bar.