2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75695We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for stabilization and asymptotic stabilization by applying a fast oscillating control to the string. In the first situation studied we assume that system is subject to a damping force; next we consider the system without damping. We extend the tools of high-order averaging and of chronological calculus for studying stability of this distributed parameter system.17 pagesAnalysis of PDEs34E05; 34C29; 34D20text