Coupled oscillators can become synchronized over time. Conditions for synchronization and the energy of a synchronized network for a simplified Kuramoto model are firstly explored by a numerical approach. Features of a network such as its coupling number, winding number, and energy are revealed through computerized simulations (using MATLAB). A correspondence between a network of identical-frequency oscillators and a spring-mass system on a ring is established. Thereafter, analytical approaches are used to describe the energy and winding number of a network. Lastly, the stability of the equally-spaced equilibrium solution of the network is characterized by establishing the dependence of the eigenvalues of a network on the coupling number and the number of oscillators.