In this paper, we carry out a detailed investigation of a recently discovered effect of the increase in the ferromagnetic resonance (FMR) amplitude for cobalt-palladium layered films in the presence of hydrogen gas (H₂). We find that this effect is not correlated with the FMR peak shift in the presence of H₂ found previously. This follows from observation of a vanishing shift but a change in the amplitude of 69.5% for a sample having a 70 nm thick cobalt layer studied in this paper. The change in amplitude is found to be mainly due to the narrowing of the FMR linewidth, which has its origin in a change in the damping parameter $α $. The increase in the amplitude allows us to measure H₂ concentration in nitrogen as a carrier gas in a very broad range--from 0.05% to 70% with sensitivity higher than in our previous papers.