The excitation of neutron stars is expected to be an important source of gr
avitational radiation. Therefore it is of fundamental importance to investi
gate mechanisms that trigger oscillations in neutron stars in order to char
acterize the emitted radiation. We present results from a numerical study o
f the even-parity gravitational radiation generated from a particle orbitin
g a neutron star. In contrast to previous calculations performed in the Fou
rier domain, we use the direct time evolution of the perturbation equations
. We focus our investigation on those conditions on the orbital parameters
that favor the excitation of w modes. We fmd that for astrophysically reali
stic conditions, there is practically no w-mode contribution to the emitted
radiation. Only for particles with ultrarelativistic orbital speeds greate
r than or equal to0.9c does the w-mode significantly contribute to the tota
l emitted gravitational energy. We also stress the importance of setting co
nsistent initial configurations.