For the two degree-of-freedom system shown in Figure 6.71, determine the natural frequencies of oscillation about equilibrium and the respective modal ratios. Assume the following parameter values: \(m_{1}=10 \mathrm{~kg}, m_{2}=14 \mathrm{~kg}, k_{1}=4 \mathrm{~N} / \mathrm{m}, k_{2}=5\) \(\mathrm{N} / \mathrm{m}\), and \(k_{3}=6 \mathrm{~N} / \mathrm{m}\).

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6000 k k T 6000 m 6000 k T Figure 6.71: Two degree-of-freedom system.