The purpose of this paper is to study various monotonicity conditions of the
period function T(c) (energy-dependent) for potential systems x¨+g(x)=0 with a center at the origin 0. We had before identified a family of new
criteria noted by (Cn​) which are sometimes thinner than those previously
known ({\it Period function and characterizations of Isochronous
potentials}\quad arXiv:1109.4611). This fact will be illustrated by examples.Comment: 9 page