In the inverse problem with uncertainty, suppose that instead of a fixed constraint, we take an elastic constraint in order to generate an additional equation (as shown in Figure 9.58). The benefit of using a spring as a constraint, rather than just fixing mass \(m_{2}\) as in Figure 9.52, is that \(k_{3}\) can be varied to represent a free end using \(k_{3}=0\), or a fixed end using \(k_{3}=\infty\). Derive the ratios needed to estimate the mean values and variances of the structural parameters. Assume that each mass is exactly \(20 \mathrm{~kg}\).

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k K3 m mo 123 www Figure 9.58: Two degree-of-freedom system.