A special problem of optimal control connected with damping of enforced oscillations has been considered. There are some nonconvex quadratic integral constraints in the form of equalities and inequalities in the settlement of the problem. The external disturbance, coefficients of quadratic forms and system coefficients are assumed to be almost periodic time functions. It has been shown that the Lagrange duality method is correct for the nonconvex problem of global optimization. It is the basis of effective algorithms for solving this problem.