On the construction site for a new skyscraper, a uniform beam of steel is suspen

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Science

Description

On the construction site for a new skyscraper, a uniform beam of steel is suspended from one end. If the beam swings back and forth with a period of 2.48 s, what is its length?

 m

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Explanation & Answer

Look up the theory of vibration of uniform 1D continuous systems (specifically vibration of uniform bars) for the details. For the situation described above, the beam acts as a cantilever vibrating in 1st mode, For theory of vibration of cantilever, beta*L=1.776 for mode 1 where L=length Also, w=(beta^2)*sqrt(EI/rho*A) where w=natural frequency, EI =flexural rigidity, rho=density, A=area of cross-section. In this case, calculate w from given T, and with known material properties (EI, rho) back calculate the length.


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