  Periodic excitation of electron spin polarization by consecutive laser pulses
in phase with Larmor spin precession about a magnetic field results in resonant
spin amplification (RSA). We observe a drastic modification of RSA in $n$-doped
bulk GaAs under the influence of external oscillating magnetic field. We find a
double-peaked electron spin resonance instead of a single-peaked resonance
expected without optical pumping. The frequency splitting increases linearly
with amplitude of field oscillations, while the spin deviation increases
quadratically. Moreover, we show that the oscillating field can both
significantly suppress RSA and induce new conditions for resonance. Using
quaternions to describe spin rotations, we develop a theory that simultaneously
considers spin precession, decay, and amplification and reproduces the entire
set of the experimental data. Using the radio-frequency field allows one to
control the conditions of RSA and achieve fine tuning of average spin
polarization without modifying the parameters of optical pumping.
