Here we have left the impurity painted blue, but briefly set the impurity mass equal to the host mass. "born" tries to make an unreasonably narrow packet, with the consequence that with run the energy quickly disperses over the whole chain.
Now set the impurity mass to 0.5 and run again. There is a small amount of "trash" that moves out into the chain (we haven't set the initial conditions quite right) but then the localized impurity mode continues to ring without dispersion or dissipation.
Zoom the graph to a couple of cycles of the motion near t = 400. How do the amplitude and phase of the motion of atoms vary as you move from atom to atom along the chain?