  We studied the orbit of an electron revolving around an infinitely massive
nucleus of a large classical Hydrogen atom subject to an AC electric field
oscillating perpendicular to the electron's circular orbit. Using perturbation
theory in geometric algebra, we show that the equation of motion of the
electron perpendicular to the unperturbed orbital plane satisfies a forced
simple harmonic oscillator equation found in Lorentz dispersion law in Optics.
We show that even though we did not introduce a damping term, the initial
orbital position and velocity of the electron results to a solution whose
absorbed energies are finite at the dominant resonant frequency
$\omega=\omega_0$; the electron slowly increases its amplitude of oscillation
until it becomes ionized. We computed the average power absorbed by the
electron both at the perturbing frequency and at the electron's orbital
frequency. We graphed the trace of the angular momentum vector at different
frequencies. We showed that at different perturbing frequencies, the angular
momentum vector traces epicyclical patterns.
