A video camera, of mass \(2.0 \mathrm{~kg}\), is mounted on the top of a bank building for surveillance. The video camera is fixed at one end of a tubular aluminum rod whose other end is fixed to the building as shown in Fig. 3.50. The wind-induced force acting on the video camera, \(f(t)\), is found to be harmonic with \(f(t)=25 \cos 75.3984 t \mathrm{~N}\). Determine the cross-sectional dimensions of the aluminum tube if the maximum amplitude of vibration of the video camera is to be limited to \(0.005 \mathrm{~m}\).

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0.5 m Video camera Fo cos wt Building Tubular aluminum rod FIGURE 3.50 Aluminum rod supporting a video camera.