We present a novel approach for studying the dynamics of a superconducting
qubit in a cavity. We succeed in linearizing the Hamiltonian through the
application of an appropriate unitary transformation followed by a rotating
wave approximation (RWA). For certain values of the parameters involved, we
show that it is possible to obtain a a Jaynes-Cummings type Hamiltonian. As an
example, we show the existence of super-revivals for the qubit inversion
