The cantilever beam in Figure 2.32 undergoes harmonic oscillation, being driven by a force of amplitude \(A\) and nominal frequency \(\omega\). An examination of a long time-history of the response shows slight fluctuations about an exact harmonic response. If we divide this long time-history into segments of one period \((2 \pi / \omega)\) and superpose these, we obtain the set of curves shown in Figure 2.33. How serious are such fluctuations in the response of the beam? Is there a way to relate the magnitude of the fluctuation to the maximum response? What would be a reasonable way to specify the value of \(\omega\) ?

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F(t) = A cos cot Figure 2.32: Cantilever beam vibrating under harmonic loading.