We report a particle dynamics based simulational study of the propagation of [Formula presented] function mechanical impulses in idealized three-dimensional hexagonal close packed lattices of monosized Hertz spheres. This paper presents five key results on the kinetic energy of grains at the surface of a granular bed after the generation of a normal impulse into the bed. (i) We find that the time integrated or cumulative average kinetic energy per surface grain, [Formula presented], drops as an impulse penetrates into the bed. The minimum value of [Formula presented], say [Formula presented], is reached at some time [Formula presented] after the impulse has been generated. (ii) This value, [Formula presented], depends upon the restitutional losses at the grain contacts and [Formula presented] increases as restitutional losses at granular contacts increase in magnitude. (iii) The asymptotic value of [Formula presented] is denoted by [Formula presented]. Our data show that increasing the area across which an impulse is generated, [Formula presented], leads to [Formula presented]. (iv) If we assign random masses to our monosized grains, [Formula presented] grows quadratically as a function of the range of mass variation about a mean mass. We find that at large times, i.e., [Formula presented], [Formula presented], where the constant [Formula presented] is roughly independent of restitution for the typical values of restitution encountered. (v) Our data suggest that at early times, the backscattering process carries signatures of ballistic propagation of the mechanical energy while at late times, the backscattering process is reminiscent of vibrations of an essentially ergodic system. Given the ballisticlike propagation of mechanical energy into granular beds, we conclude that a wave equation based description of mechanical energy propagation into granular beds may not always be appropriate. © 2004 The American Physical Society.