Transverse vibration of a simply supported beam with symmetric overhang of arbitrary length

The numerical solution to the frequency equation for the transverse vibration of a simple beam with symmetric overhang is found. The numerical results converge to the analytical solutions for the two limiting cases of a beam with no overhang and a beam with no span and agree with the case in which the supports are at the nodal points of a freely vibrating beam. An approximation to the solution of the frequency equation for beams with small overhang is presented and compared to the numerical solution. This simple yet accurate approximation is most useful to determine a beam's flexural stiffness, EI or modulus of elasticity, E, by freely vibrating a simply supported beam.