The classical behavior of two interacting particles in the presence of a uniform magnetic field is
studied in the small oscillations approximation. Using the Lagrangian formalism, the equations of
motion are derived, as are their solutions and constants of motion. Normal modes of oscillations and
their corresponding normal coordinates are obtained that strongly depend on the initial condition;
therefore, we observe that the oscillation along the line that joins the particles is
non-isochronous. In addition, particular attention has been paid to the planar motion, without the
pseudomomentum component parallel to the magnetic field, where one longitudinal mode and two
transversal modes are obtained.