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When considering buildings, it is important to identify the natural frequencies of beams. The implication will...

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Question

Physics

When considering buildings, it is important to identify thenatural frequencies of beams. The implication will be that rotatingequipment (e.g. pumps, compressors, washing machines, etc.) areselected so that the natural frequency of the beam is not excitedthus brining the entire structure into resonance and causingdamage.

A beam will have an infinite number of natural frequencies. Thenatural frequencies of a beam are the roots of a characteristicequation (which can be obtained using various analytical methods).Consider a beam whose characteristic equation is given by:

cos(0.1012x)cosh(0.1012x)=1

where x is the natural frequency in Hz.

Problem :

Use the Newton-Raphson method to find the natural frequency ofthe beam near 46 Hz.

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