If the ground in Fig. 3.57, is subjected to a horizontal harmonic displacement with frequency \(\omega=200 \mathrm{rad} / \mathrm{s}\) and amplitude \(X_{g}=15 \mathrm{~mm}\), find the amplitude of vibration of the floor (mass m). Assume the mass of the floor as \(2000 \mathrm{~kg}\) and the stiffness of the columns as \(0.5 \mathrm{MN} / \mathrm{m}\).

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22 m (1) - A cos cot FIGURE 3.57 - 82 Single story building subjected to ground acceleration.