Hi, AskScience! I'm trying to figure out a simple approximation for a complex problem, but I'm having a lot of trouble assigning physical meaning to the math behind it.

Given a closed system of charged particles in vacuum under an electric field, the charged particles will respond to the electric field and migrate towards the appropriate electrodes. However, as they get closer to the electrodes, the force from the electric field will start to compete with the Coulombic repulsion. I expect that these will cause the particles to bounce back and forth in some sort of decaying harmonic fashion.

How can I roughly figure out the strengths of that oscillation and the timescale?

Thanks!