A cantilever beam with an end mass \(m\) is fixed at the top of a multistory building to measure the acceleration induced at the top of the building during wind and earthquake loads (see Fig. 10.48). Design the beam (i.e., determine the material, cross-sectional dimensions, and the length of the beam) such that the stress induced in the beam should not exceed the yield stress of the material under an acceleration of \(0.2 \mathrm{~g}\) at the top of the building. Assume that the end mass \(m\) is equal to one-half of the mass of the beam.

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m = y(t) Y sin wot FIGURE 10.48 Cantilever beam with end mass fixed on top of building.