This is too long for a comment, so here it goes:
What causes a valence electron of a large atom to feel an effective attractive potential that is similar to a harmonic oscillator?
I hope people following this forum at least understand that in order to have electrons around nuclei display a stable solution and form an atom, a potential is necessary.
This potential is very complicated since it is the result of a many body problem.
Fortunately we have mathematical tools to help us estimate the potential of a valence electron by the following logic:
The unknown real potential must be well behaved since the atom is stable and therefore it can be expanded in a Taylor series expansion in the variable of interest, call it r, the radial variable for the potential.
The first few terms are dominant in the series for r<1. The potential must be symmetric because no large asymmetries have been observed in atoms, thus the coefficient of the r term must be zero. The first power that is the strongest in the expansion ( by the form of a Taylor expansion) is the r^2 which is the function of a harmonic oscillator potential, well studied with the Schrodinger equation.
In a first approximation in quantum mechanics, all attractive symmetric potentials have as a dominant term the harmonic oscillator functional form thus one can use the language of a "restoring force" , because a spring is a harmonic oscillator and the terminology carries over.
To address the "resonate" part: a harmonic oscillator restores i.e. pulls back the particle and it does so even in classical physics with a certain frequency ( think of a spring again). In quantum mechanics there still is a frequency associated with the position of the electron's orbital. When the disturbance is of the same frequency as the frequency of the potential solution for the electron one can have a resonance phenomenon.