The purpose of this thesis is the characterization of dynamics of the superconducting phase emerging from a semiclassical description of a superconducting circuit composed by two Josephson junctions in series, in the presence of an external voltage source. The topology of the circuit identifies two superconducting leads and a central superconducting island. Starting from a semiclassical Lagrangian derived by a lumped element description of the superconducting circuit, the Hamiltonian is then derived and, consequently the Hamilton's equations. Further manipulations of the latter leads to a non-linear second order differential equation controlling the evolution of the island superconducting phase. The Resistive and Capacitatively Shunted Junction (RSCJ) model has been used to take account of the dissipation in the system.