These electrons are mostly ~1 metre apart from each other. Considering that they will be moving at something like 6e6 m/s (to use Sylas's figures), the average electron is going to be passing by an average of 6e6 electrons per second. This means that the net force exerted on any particular electron, including our deflected electron, is going to be changing incredibly fast, and in a totally chaotic manner. There is no way a single electron can perform SHM under these circumstances.

Edit to change wording.