Final answer:
The primary factor influencing the frequency of oscillation of a conducting sphere between two plates is the voltage across the plates, as it directly affects the electric field strength and thus the force on the sphere.
Step-by-step explanation:
In the context of an oscillating conducting sphere between two plates, the factor that primarily influences the frequency of the oscillation is the voltage across the plates. The mass of the sphere, the charge on the sphere, and the distance between plates do have an impact on the system, but the oscillation frequency, which is related to the acceleration and force experienced by the sphere, is most directly affected by the electric field created by the voltage difference. An increase in the voltage will result in a stronger electric field, which can cause the sphere to oscillate at a higher frequency.
The conductive nature of the sphere indicates that when placed between two plates with a voltage applied, charges in the sphere will be influenced to move, causing it to oscillate. The mass of the sphere will affect the inertia of the system, the charge on the sphere can influence the amount of force it experiences, and the distance between the plates influences the strength of the electric field across a given distance, but it is the voltage that drives the change in potential energy necessary for oscillation to occur.