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?

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.