Electro-SHM

Consider a charged particle which has mass $m$ and a positive charge present on it having magnitude as $+q$ .It is placed midway between $2$ positively charged particles each having a charge of $Q$ ,one of which is placed at co-ordinates $(x,y)$ $=$ $(+a,0)$ and the other at co-ordinates $(x,y)$ $=$ $(-a,0)$ where $a$ is a real constant.The particle is slightly displaced from the equilibrium position by a distance $x$ along the x-axis,where $x << a$ .It will then simple harmonically oscillate with a time period $t$ given by the expression

where $\alpha$ and $\beta$ are positive integer constants. What is $\alpha$ $+$ $\beta$ ?

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Details and Assumptions:

1) $\epsilon_0$ refers to the permittivity constant.

2) $\alpha$ and $\beta$ are co-prime integers.

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Inspired by this problem and by this problem .