  An analytical form of the characteristic equation for a vertically mounted
cantilever beam with an end rigid body is obtained and solved for the
eigenvalues of the structure. The effect of the weight of the structure is
taken into consideration by estimating the load as a function of the length of
the beam. The mass, rotary inertia and eccentricity of the end rigid body are
demonstrated to considerably affect the eigenvalues of the structure.
