  A semi-numerical method is used in order to locate the position and calculate
the period of periodic orbits in a 3D composite bisymmetrical potential, in a
number of resonant cases. The potential consists of a 3D harmonic oscillator
and a Plummer sphere. The outcomes are compared with results found using the
numerical integration of the equations of motion and the agreement is very
good. This agreement strongly suggests, that semi-numerical methods can be used
in order to obtain fast and reliable results regarding the position and period
of the periodic orbits in 3D composite potentials with a harmonic oscillator
part and different kinds of perturbations. Comparison with other methods of
obtaining 3D periodic orbits is discussed.
