Since a few years there is an increasing interest in minimizing the energy consumption of computing systems. However in a shared computing system, users want to optimize their experienced quality of service, at the price of a high energy consumption. In this work, we address the problem of optimizing and designing mechanisms for a linear combination of weighted completion time and energy consumption on a single machine with dynamic speed-scaling. We show that minimizing linear combination reduces to a unit speed scheduling problem under a polynomial penalty function. In the mechanism design setting, we define a cost share mechanism and studied its properties, showing that it is truthful and the overcharging of total cost share is bounded by a constant.