An automobile, having a mass of \(1000 \mathrm{~kg}\), runs over a road bump of the shape shown in Fig. 4.49. The speed of the automobile is \(50 \mathrm{~km} / \mathrm{h}\). If the undamped natural period of vibration in the vertical direction is \(1.0 \mathrm{~s}\), find the response of the automobile by assuming it as a single-degree-of-freedom undamped system vibrating in the vertical direction.

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Height of bump (m) 0.1 0 0.25 FIGURE 4.49 Triangular road bump. 0.50 Distance along road (m)