A steel cantilever beam of diameter \(2 \mathrm{~cm}\) and length \(1 \mathrm{~m}\) is subjected to an exponentially decaying force \(100 e^{-0.1 t} \mathrm{~N}\) at the free end, as shown in Fig. 8.35. Determine the steady-state response of the beam. Assume the density and Young's modulus of steel as \(7500 \mathrm{~kg} / \mathrm{m}^{3}\) and \(210 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\), respectively.

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2 cm dia. 100e 0.1 N 1 m FIGURE 8.35 Cantilever beam with force applied at end.