Consider the two identical longitudinally vibrating uniform beams shown in Figure 7.50 connected by a linear spring. Derive the frequency equation, the first three natural frequencies, and plot the first three mode shapes for axial vibration. Use \(k L / E A=0.1\).

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m, EA, L k m, EA, L x1 X2 Figure 7.50: Two identical cantilever beams connected by a spring.