Why is mass included in the period calculation of SHM for point charges?

[Ronnin]

This is a question I already solved but was curious about something. There are two positive point charges of the same maginitude on the same axis. They are some distance appart with third point positive charge placed slightly off the midpoint between the two original charges. The question is to find the period of the SHM. In solving this I basically applied Coulumb's law as the restoring force. After looking at the answer the book gave I noticed it still had a variable for mass included. My question is why would mass even come into play for a system composed of point particles with electric force? If gravity is neglected, couldn't I just apply the the particle's charges in place of mass?

 

[Mindscrape]

Are you referring to how the electric force is generally much stronger than the gravitational force, so why we even care about the gravitational force? In general, if I am understanding what you are asking about, you are right and the gravitational force probably won't have much of an effect. Nonetheless, if you want to examine the particle's motion of long periods of time the gravitational force might need to be included; for example, gravity might damp the SHM.

 

[Ronnin]

The question ignores gravity and does not even define a mass for any of the charges (they are all treated as positive point particles). The solution in the book still included a "m" for mass as though it would matter for a system such as this one.

 

[Mindscrape]

Hmm, I would have to see the problem, but I don't see anything irregular with having mass constants in your solutions - particularly if they are in the angular frequency.