In this paper a simple tabular method is developed by which the vibration amplitudes, bending moments, and shear forces of a beam of variable but symmetrical cross section, carrying any number of concentrated masses and acted on by any number of harmonically varying forces, can be found. The driving forces must all have the same frequency but the phase angles may be different. The method is an extension of the one employed by the author to find natural modes of vibration of beams, but in the case of forced vibration only one application of the tabular calculations is necessary, making it essentially a far simpler problem than that of finding the natural modes. Internal damping of the beam material is easily considered and should always be taken into account if there is any danger that the forced frequency is near any one of the natural frequencies.

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