Consider a 2-DOF isolation system model with m=mb, fixed base period 2 sec., isolation system period 2 sec. Compute the periods of the two modes of the combined system by the exact formula, and the first order ? approximation. Compare the exact and approximate solution results.

2. For the same problem, assuming damping of 2% for the structure, if fixed base, 30% for the isolation system, estimate the maximum structure drift, the maximum isolator displacement, and the base shear coefficient for the El Centro 1940 record. Compare each with the corresponding fixed-base response.

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[a]'s Response Spectrum for the El Centro Record (N-S) of the 1940 Imperial Valley Earthquake 2.5 1.5 0.5 0.5 1.5 Period [sec] 2.5 3.5 B=0 B=0.02 B=0.05 B-0.10 B0.15 B=0.20 B-0.30 [a]'s Response Spectrum for the El Centro Record (N-S) of the 1940 Imperial Valley Earthquake 2.5 1.5 0.5 0.5 1.5 Period [sec] 2.5 3.5 B=0 B=0.02 B=0.05 B-0.10 B0.15 B=0.20 B-0.30