Design a seismometer of the type shown in Fig. 4.75 (a) (by specifying the values of \(a, m\), and \(k\) ) to measure earthquakes. The seismometer should have a natural frequency of \(10 \mathrm{~Hz}\), and the maximum relative displacement of the mass should be at least \(2 \mathrm{~cm}\) when its base is subjected to the displacement shown in Fig. 4.75(b).

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Cage (mass negligible) y(t) 000000 k/2 8k/2 Rigid bar (mass negligible) m x(t) 1 y(t), cm 1 0 1 b = 3a (a) FIGURE 4.75 Seismometer with base displacement. (b) t, S