The invention relates to a machine (1) having a machine frame (2), mobile by means of on-track undercarriages (3) on rails (4) of a track grid (5), and a stabilizing unit (8) which comprises a vibration exciter (15) for generating horizontal vibrations extending transversely to the longitudinal direction of the machine and flanged rollers (10) designed to roll on the rails (4). In this, a camera (11) is mounted on the machine frame (2) for recording a section of the track grid (5) set in vibrations, wherein the camera (11) is connected to an evaluation device (16) in order to derive from the recorded image data a resulting deflection (sr) of the track grid (5). In this manner, the amplitude (ar) of the sleeper deflection can be recorded, which is a measure of the actually effective vibration for stabilizing the track.