The ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2.

Any kind of frequency, including the angular kind, is closely involved with
time. Still, for some unknown reason,you've given us no time information
whatsoever ... a peculiar decision on your part, since we can be sure that
it's right there, inexorably intertwined with the part of the question that you
DID copy and share with us. 

Furthermore and moreover, for one with no prior experience with simple
harmonic motion, the many symbols in this question such as ' d ', ' a ',
' << ', ' d₂ ', and ' a₂ ' would be of no help at all to guide him toward a
solution.  On the contrary, he would conclude that the question itself
had been posted by some alien life form.

To sum up:  Come back and post the drawing that goes along with the
question, make sure you have presented all of the information that the
question includes, and then we'll talk.