An object of mass M is attached to a spring with spring constant k whose unstretched length is L, and whose far end is fixed to a shaft that is rotating with angular speed omega. Neglect gravity and assume that the mass rotates with angular speed omega as shown. (Intro 1 figure) When solving this problem use an inertial coordinate system, as drawn here. (Intro 2 figure) Given the angular speed omega, find the radius R(omega) at which the mass rotates without moving toward or away from the origin.
Express the radius in terms of k, L, M, and omega.