We analyze the time-behaviour of the Gaussian wave packet of a quantum part
icle moving in the field of a linear force, undergoing a continuous nondemo
lition observation of its position. In particular, the time-dependence of p
osition and momentum dispersions, as well as position-momentum uncertainty
is investigated. The discussion includes the case of a free particle and in
itially coherent state of a harmonic oscillator. It is found that in the be
ginning of observation the momentum dispersion and position-momentum uncert
ainty always increase in contrast to the position dispersion. It is also pr
oved that all considered functions asymptotically take the form of harmonic
oscillations, decaying to finite values. For initially coherent states, th
e asymptotic bounds for all considered functions are given.