  Coordinate-transformation-inspired optical devices have been mostly examined
in the continuous-wave regime: the performance of an invisibility cloak, which
has been demonstrated for monochromatic excitation, %would inevitably is likely
to deteriorate for short pulses. Here we investigate pulse dynamics of flexural
waves propagating in transformed plates. We propose a practical realization of
a waveshifter and a rotator for flexural waves based on the coordinate
transformation method. Time-resolved measurements reveal how the waveshifter
deviates a short pulse from its initial trajectory, with no reflection at the
bend and no spatial and temporal distortion of the pulse. Extending our
strategy to cylindrical coordinates, we design a wave rotator. We demonstrate
experimentally how a pulsed plane wave is twisted inside the rotator, while its
wavefront is recovered behind the rotator and the pulse shape is preserved,
with no extra time delay. We propose the realization of the dynamical mirage
effect, where an obstacle appears oriented in a deceptive direction.
