  We study the generation of excitations due to an ''impurity''(static
perturbation) placed into an oscillating Bose-condensed gas in the
time-dependent trapping field. It is shown that there are two regions for the
position of the local perturbation. In the first region the condensate flows
around the ''impurity'' without generation of excitations demonstrating
superfluid properties. In the second region the creation of excitations occurs,
at least within a limited time interval, revealing destruction of
superfluidity. The phenomenon can be studied by measuring the damping of
condensate oscillations at different positions of the ''impurity''.
