A bead of mass m and having a charge q0 can move without friction along a thread stretched horizontally

A bead of mass m and having a charge q0 can move without friction along a thread stretched horizontally between two identical point charges q of the same sign. Thread length 2l. Determine the frequency ω of small longitudinal vibrations of the bead about the equilibrium position.

First, we calculate the resulting force when the bead is displaced (1). Then we come to an approximate equality, provided that | x | << l (2). And through the square of the natural angular frequency of vibrations, we calculate the frequency ω of small longitudinal vibrations of the bead (3). It will be equal to ω / (2π).