Question: A uniform fixed-fixed beam of length (l) with a rectangular cross section (w times h) is shown in Fig. 7.17. Assuming the Young's modulus as

A uniform fixed-fixed beam of length $l$ with a rectangular cross section $w \times h$ is shown in Fig. 7.17. Assuming the Young's modulus as $E$ and unit weight as $\gamma$ for the material of the beam and the deflection shape as

\[y(x)=C\left(1-\cos \frac{2 \pi x}{l}\right)\]

Determine the natural frequency of the beam.

y(x) x FIGURE 7.17 Beam with rectangular section. -W Cross section

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