  We hereby introduce and study an algorithm able to search for initial
conditions corresponding to orbits presenting forced oscillations terms only,
namely to completely remove the free or proper oscillating part.
  This algorithm is based on the Numerical Analysis of the Fundamental
Frequencies algorithm by J. Laskar, for the identification of the free and
forced oscillations, the former being iteratively removed from the solution by
carefully choosing the initial conditions.
  We proved the convergence of the algorithm under suitable assumptions,
satisfied in the Hamiltonian framework whenever the d'Alembert characteristic
holds true. In this case, with polar canonical variables, we also proved that
this algorithm converges quadratically. We provided a relevant application: the
forced prey-predator problem.
