Kevin Zhou — Mechanics IV Problem 3 · Kevin Zhou #M4.3
Physics · mechanics
Problem
Problem 1 (Morin 5.13). A hole of radius R is cut out from an infinite flat sheet with mass per
unit area σ. Let L be the line that is perpendicular to the sheet and that passes through the center
of the hole.
(a) What is the force on a mass m that is located on L, a distance x from the center of the hole?
(Hint: consider the plane to consist of many concentric rings.)
(b) Now suppose the particle is releasedfrom restatthis position. Ifx ≪ R, findthe approximate
angular frequency of the subsequent oscillations.
(c) Now suppose that x ≫ R instead. Find the period of the resulting oscillations.
(d) Now suppose the mass begins at rest on the plane, but slightly displaced from the center. Do
oscillations occur? If so, what is the approximate frequency?