This paper investigates the human ability to perform rhythmic jumping on a vertically vibrating platform by analysing kinetics and kinematics. Ten test subjects participated, performing jumping on both non-vibrating and vibrating platforms. Vibration frequencies of 2.0, 2.4, and 2.8 Hz were used, with a vibration level of 2 m/s2. The frequency of jumping matched the vibration frequency, and for the first time, the jumps were timed relative to the platform's position in the vibration cycle. A metronome prompted landings at four target positions: (i)reference position and on the way down (mid-down), (ii)lowest position (trough), (iii)reference position and on the way up (mid-up), and (iv)highest position (peak), at each frequency. The study compared the achievement of the target frequency of jumping between non-vibrating and vibrating platform conditions for each frequency. Results showed the worst performance when the target frequency was 2.8 Hz on the non-vibrating platform, confirming the difficulty of faster jumping on non-vibrating surfaces. The discrete relative phase analysis revealed a preference for landing at the trough and mid-up positions on the vibrating platform, particularly at 2.8 Hz. The preferred timing of jumps corresponded to greater toe clearance and impact ratio, but shorter contact duration compared to the non-vibrating platform. These findings hold promise for improving human-structure interaction models for assembly structures used in sports and musical events.