Two equal mass particles are connected by a spring and are executing simple harmonic motion when they are placed in a horizontal, frictionless open pipe rotating at a constant angular velocity about a vertical axis through its midpoint. The midpoint of the spring is initially at the midpoint of the pipe, but neither the particles nor the spring are attached to the pipe. (a) Find the maximum angular velocity for which the particles stay in the pipe. (b) Assume (a) is satisfied and the particles stay in the pipe. Find their positions as a function of time.