Problem 1. A one-story building g with mass M, stiffness K, and damping C is modeled as a single- degree-of-freedom oscillator. The natural frequency ? and damping ratio Z of the oscillator are respectively defined by K = C M and Z = 2KM Suppose M, K, and C have the following second-moment properties: Variable (Units) Mean C.O. V Correlation Coefficients K M C K (kN/m) 500 0.33 1.0 0.3 0.0 M (kNs2/m) 2 0.25 0.3 1.0 0.0 C(kNs/m) 4 0.4 0.0 0.0 1.0 (a) Using first-order approximations, compute the means and standard deviations of ? and Z, and the correlation coefficient between them. Which parameters contribute most to the uncertainties in ? and Z