The dynamics of hydrogen bubbles produced via electrolysis in acidic electrolytes is studied in a combination of experiments and numerical simulations. A transition from monotonic to oscillatory bubble growth is observed after 2/3 of the bubble lifetime, if the electric potential exceeds -3 V. This work analyzes characteristic features of the oscillations in terms of bubble geometry, the thickness of the microbubble carpet, and the oscillation frequency. An explanation of the oscillation mechanisms is provided by the competition between buoyancy and electric force, the magnitude of which depends on the carpet thickness. Both the critical carpet thickness at detachment and the oscillation frequencies of the bubble as predicted by the model agree well with the experiment.