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The natural frequencies of a uniform cantilever beam are related to the roots βi of the frequency equation f(β) = cosh β cos β + 1 = 0, where
Determine the lowest two frequencies of a steel beam 0.9 m long, with a rectangular cross section 25 mm wide and 2.5 mm in. high. The mass density of steel is 7850 kg/m^{3} and E = 200 GPa.
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