  Important information for the roton-maxon spectrum of a flattened dipolar
Bose-Einstein condensate is extracted by applying a static perturbation
exhibiting a periodic in-plane modulation. By solving the Gross-Pitaevskii
equation in the presence of the weak perturbation we evaluate the linear
density response of the system and use it, together with sum rules, to provide
a Feynman-like upper-bound prediction for the excitation spectrum, finding
excellent agreement with the predictions of full Bogoliubov calculations. By
suddenly removing the static perturbation, while still maintaining the trap, we
find that the density modulations -- as well as the weights of the
perturbation-induced side peaks of the momentum distribution -- undergo an
oscillatory behavior with double the characteristic frequency of the excitation
spectrum. The measurement of the oscillation periods could provide an easy
determination of dispersion relations.
