(a) A hole of radius R is cut out from an infinite flat sheet of mass density σ. Let L be the line that is perpendicular to the sheet and that passes through the center of the hole. What is the force on a mass m that is located on L, at a distance x from the center of the hole?

(b) If a particle is released from rest on L, very close to the center of the hole, show that it undergoes oscillatory motion, and find the frequency of these oscillations.

(c) If a particle is released from rest on L, at a distance x from the sheet, what is its speed when it passes through the center of the hole? What is your answer in the limit x >>R?