A building frame is subjected to a blast load, and the idealization of the frame and the load are shown in Fig. 4.14. If \(m=5000 \mathrm{~kg}, F_{0}=4 \mathrm{MN}\), and \(t_{0}=0.4 \mathrm{~s}\), find the minimum stiffness required if the displacement is to be limited to \(10 \mathrm{~mm}\).

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F(t) k 22 m 2 x(t) F(t) Fo 0 to (b) (a) FIGURE 4.14 Building frame subjected to a blast load.