Using molecular dynamics a glass of soft spheres, quenched to zero tem
perature, is produced and its vibrational behaviour investigated by an
analysis of the normal modes. In addition to localized modes with hig
h frequencies, one finds (quasi)localized modes with low frequencies w
hich are centred around structural anomalies of the glass. The glass i
s then heated in stages to 12.5% of the glass temperature and is allow
ed to relax. In the relaxed glasses, again (quasi)localized low-freque
ncy modes are found, with effective masses ranging upward from about 1
0 atomic masses as in the original glasses. The observed relaxations h
ave similar effective masses and are closely related to the (quasi)loc
alized vibrations.