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.