For Example 9.13, derive the expressions for (mu_{k_{1}}) and (sigma_{k_{1}}^{2}). Example 9.13 An Uncertain Two Degree-of- Freedom

For Example 9.13, derive the expressions for \(\mu_{k_{1}}\) and \(\sigma_{k_{1}}^{2}\).

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Example 9.13 An Uncertain Two Degree-of- Freedom System Use the two-term Taylor series approximation and the following data to demonstrate the procedure developed in Section 9.13. The eigenvalues = 0.382 Hz, A = 2.618 Hz are for the original system shown in Fig- ure 9.51, and =1.000 Hz is for the system with the fixed end shown in Figure 9.52. Assume m+m2 = 20 kg exactly with zero standard deviation, where the mean values of m and m, are each 10 kg, the stiffnesses are k = k = 10 kg/cm, and all A values are approximate and assumed random with a 1% variation - that is, with coefficients of variation =/=0.01.