Introducing elasticity in the mechanical design can endow robots with the ability of performing efficient and effective periodic motions. Yet, devising controllers that can take advantage of such elasticity is still an open challenge. This letter tackles an instance of this general problem, by proposing a control architecture for executing goal-oriented and efficient point-to-point periodic motions. This is achieved by (i) producing motor torques that excite intrinsic modal oscillations, and simultaneously (ii) adjusting parallel elasticity so to shape the natural modes. Analytical proofs of convergence are provided for the linear approximation. The performance and efficiency (in the sense of low energy expenditure) of the method in the nonlinear case are assessed with extensive simulations and experiments.