Find the horizontal displacement of the floor (mass \(m\) ) of the building frame shown in Fig. 3.57 when the ground acceleration is given by \(\ddot{x}_{g}=100 \sin \omega t \mathrm{~mm} / \mathrm{s}^{2}\). Assume \(m=2000 \mathrm{~kg}\), \(k=0.1 \mathrm{MN} / \mathrm{m}, \omega=25 \mathrm{rad} / \mathrm{s}\), and \(x_{g}(t=0)=\dot{x}_{g}(t=0)=x(t=0)=\dot{x}(t=0)=0\).

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