  Using a scaling transformation we exactly determine the dynamics of an
harmonically confined Tonks-Girardeau gas under arbitrary time variations of
the trap frequency. We show how during a one-dimensional expansion a
``dynamical fermionization'' occurs as the momentum distribution rapidly
approaches an ideal Fermi gas distribution, and that under a sudden change of
the trap frequency the gas undergoes undamped breathing oscillations displaying
alternating bosonic and fermionic character in momentum space. The absence of
damping in the oscillations is a peculiarity of the truly Tonks regime.
