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A Hamiltonian approach to the parametric excitation

We propose a solution of the parametrically excited oscillator problem using the Hamiltonian formalism introduced by Glauber. The main advantage is that, within the framework of this formalism, the different possible approximations appear much more naturally than in the standard textbook presentation. Experiments on adiabatic and resonant parametric excitations of a pendulum are presented as an illustration, with particular attention being paid to the role played by the phase of the excitation.