In Example 6.7 evaluate \(\bar{C}_{1}, \bar{C}_{2}, \phi_{1}\), and \(\phi_{2}\) using the given initial conditions: \(x_{1}(0)=1 \mathrm{~cm}, x_{2}(0)=\) \(-1 \mathrm{~cm}, \dot{x}_{1}(0)=3 \mathrm{~cm} / \mathrm{s}, \dot{x}_{2}(0)=-2 \mathrm{~cm} / \mathrm{s}\). Use \(\sqrt{k / m}=10 \mathrm{rad} / \mathrm{s}\).

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Example 6.7 Two Degree of Freedom, Undamped Consider the system of Figure 6.8, simplified to the un- damped, unforced system in Figure 6.13. Let m = m, m = 2m, k =k, k = 2k, kg = 3k, and obtain the natural frequencies and modes of vibration.