The dynamics and the stability of a forced damped nonlinear oscillator driven at twice its resonance frequency is studied. At the transition from a dissipative system to a Hamiltonian system, simple scalings relations are found by the use of the Floquet theory of the linearized problem. The Floquet exponents and the period-doubling bifurcation point are determined analytically in the limit of small damping. The theory is compared to numerical calculations on a Duffing oscillator and excellent agreement is found.