A small sphere of mass \(m\) is attached to a string of length \(L\). The other end of the string is attached to the center of a horizontal ceiling. A smooth, rigid vertical cylindrical wall of radius \(R\) (where \(R < L\)) is centered on the attachment point of the string. The sphere is set into a horizontal circular path so that it revolves along the inside of the cylindrical wall with a constant angular speed \(\omega\). The string makes an angle \(\theta\) with the vertical, as shown in Figure 1. Friction between the sphere and the wall is negligible.