The characteristics of dynamic systems subjected to multiple linear constraints are determined by considering the constrained effects. Although there have been many researches to investigate the dynamic characteristics of constrained systems, most of them depend on numerical analysis like Lagrange multipliers method. In 1992, Udwadia and Kalaba presented an explicit form to describe the motion for constrained discrete systems. Starting from the method, this study determines the dynamic characteristics of the systems to have positive semidefinite mass matrix and the continuous systems. And this study presents a closed form to calculate frequency response matrix for constrained systems subjected to harmonic forces. The proposed methods that do not depend on any numerical schemes take more generalized forms than other research results.