A uniform thin rod of length \(L\) and mass \(M\) is suspended from a frictionless horizontal pivot located a distance \(x\) from the rod's center of mass, where \(0 < x < L/2\). The rod oscillates in a vertical plane with small angular amplitude. As \(x \to 0\), the period of oscillation approaches infinity, and as \(x\) approaches \(L/2\), the period increases after passing through a minimum. In terms of \(L\), what distance \(x\) minimizes the period of oscillation?