A variational principle, resembling that used in quantum mechanics, is formulated and applied to study the first-order correction to the period of a simple pendulum. The relevant small parameter is the ratio of the mass of the suspension cord to that of the pendulum bob. The suspension cord is assumed inextensible but otherwise both its elastic properties and mass distribution are arbitrary. Results previously derived independently for a rigid rod or flexible cord suspension are thus obtained within a single formalism. The discussion of the connection between these cases and of related results is thereby simplified.