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Two postitive charges +Q are held at fixed distance d from each other. A particle of charge -q is placed at the mid point between them and given a small displacement y, on the line perpendicular to the line joining them and released. Show that hte particle described SHM of period [tex] (\frac{\epsilon_{0} m \pi^3 d^3}{qQ})^\frac{1}{2} [/tex]

i drew a figure of what this might look like.

I was wondering if i had to prove that this particle is going to undergo SHM. I can easily say that at points +y and -y the force on the particle is the maximum and is [tex] \pm \frac{Qqd}{4 \pi \epsilon_{0} tan^2 \theta} [/tex]

would i then simply plug the acceleration of this force into th4e SHM equation??

But how would i get rid of the tan theta?? I doesnt appear in the answer they want.. after all.

i drew a figure of what this might look like.

I was wondering if i had to prove that this particle is going to undergo SHM. I can easily say that at points +y and -y the force on the particle is the maximum and is [tex] \pm \frac{Qqd}{4 \pi \epsilon_{0} tan^2 \theta} [/tex]

would i then simply plug the acceleration of this force into th4e SHM equation??

But how would i get rid of the tan theta?? I doesnt appear in the answer they want.. after all.