The electric charge of a black hole is frequently neglected in many astrophysical scenarios due to unrealistically large values of the charge necessary for the Reissner-Nordström spacetime metric. Nevertheless, a variety of selective accretion processes could result in a black hole having a gravitationally weak electric charge. Thus, the motion of charged particles can be influenced by a combined effect of gravitational attraction and electrostatic interaction, which can be attractive or repulsive. This can lead to the existence of certain observational patterns in the non-thermal spectra of astrophysical black holes. In the present work, we study the harmonic oscillations of charged particles around a weakly charged black hole.