<p>We consider a pendulum with vertical harmonic oscillation at its point of suspension. This pendulum is suspended between two vertical, infinite wires that have a uniform distribution of positive electrical charge and are equidistant from the point at which the pendulum is suspended. Assume also that bulb of this pendulum has an electrical charge. Under these conditions, the nonlinear stability of the normal equilibrium position of this system is investigated from a Hamiltonian perspective, by taking into account dimensionless parameters: the first one is related to the electrical charges, the second one is associated with the amplitude of the pendulum’s suspension point; and the third is derived from the oscillation frequency. We present methodologies that play an important role in the normalization of the Hamiltonian function, as well as some results in order to obtain information on the nonlinear stability of the normal equilibrium point without resonances, and in cases where resonance occurs.</p>