An extension of a previous test particle simulation model (Inan et al.,1978) of the gyroresonance wave-particle interaction in the magnetosphere is used to compute the detailed time variation of the precipitated energy flux induced by monochromatic short-duration VLF waves. The resulting precipitation pulse is found to have a characteristic shape dependent on the L value, a cold plasma density wave frequency, and duration, as well as the energetic particle distribution function. The role of these variables in determining the temporal variation and the magnitude of the precipitated flux is discussed for a wide range of typical magnetospheric parameters. As an example, a 400-ms wave pulse with a frequency of 6.825 kHz (equatorial half-gyrofrequency) at L=4 and for a cold plasma density of 400 el/cc produces a 3.5-s long precipitation pulse as observed at 1000 km, with the flux reaching its peak value at approximately 3.8 s after the injection of the wave at the same point. Our findings indicate that if the predicted temporal variations can be observed, the results may be used to diagnose some of the details of the energetic particle distribution in the magnetosphere. The magnitude of the precipitated flux is a function of the trapped particle distribution. For example, for typical trapped electron distribution interacting with a 5 kHz wave of 1 pT intensity at L=4 the peak precipitated energy flux is found to be 5¿10-3 ergs/cm2 s. The predicted fluxes for typical parameters are 102--103 times larger than typical background precipitation levels at these latitudes and would be detectable with presently available instruments.