Oscillating Charge (No Springs Attached)

There are three identical collinear particles of charge \((q = 10^{-6}\text{ C}) \) and mass \((m = 1\text{ kg}) \). Two of the particles are held in place at \((x = 0\text { m}) \) and \((x = 1\text{ m}) \) respectively. The third particle is free to move, and is initially positioned at \((x = \dfrac{1}{4}\text{ m}) \).

If the Coulomb constant is \((k = 9\times10^{9}\text{ Nm}^{2}\text{ C}^{-2}) \), determine the oscillation period of the moving charge (rounded to the nearest half second).

While solving, neglect all forces except for the basic Coulomb force.

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