Two identical particles each having a charge +q is fixed in place a distance d apart. A third particle of charge -Q is free to move and released from rest a distance of x along the perpendicular bisector of the original two particles.
Let us presume that x << d which gives rise to the third particle oscillating as a simple harmonic oscillator among the other two charges.
In terms of the variables of the problem,
1. Decide the period of this simple harmonic oscillation
2. Decide the speed of the particle when it is directly between the two charges.
Note that the binomial expansion may be required to solve.