  This paper reports the first simultaneous measurement of the horizontal and
vertical components of the polarization vector in a storage ring under the
influence of a radio frequency (rf) solenoid. The experiments were performed at
the Cooler Synchrotron COSY in J\"ulich using a vector polarized, bunched
$0.97\,\textrm{GeV/c}$ deuteron beam. Using the new spin feedback system, we
set the initial phase difference between the solenoid field and the precession
of the polarization vector to a predefined value. The feedback system was then
switched off, allowing the phase difference to change over time, and the
solenoid was switched on to rotate the polarization vector. We observed an
oscillation of the vertical polarization component and the phase difference.
The oscillations can be described using an analytical model. The results of
this experiment also apply to other rf devices with horizontal magnetic fields,
such as Wien filters. The precise manipulation of particle spins in storage
rings is a prerequisite for measuring the electric dipole moment (EDM) of
charged particles.
