In this paper we note the equivalence between exact controllability and exponential stabilizability for an abstract conservative system with bounded control. This enables us to establish a frequency domain characterization for the exact controllability/uniform exponential decay property of second-order elastic systems, such as the wave equation and the Petrovsky equation, with (locally) distributed control/damping. A piecewise multiplier method for frequency domain is introduced. For several classes of PDEs on regions which are not necessarily smooth, we obtain a sufficient condition for the subregion on which the application of central/damping will yield the exact controllability/uniform exponential decay property. This result provides useful information for designing the location of controllers/dampers for distributed systems with a law of conservation.