  {Three-wave resonant interactions constitute an essential nonlinear mechanism
coupling capillary surface waves. In a previous work, Haudin et al. [Phys. Rev
E 93, 043110 (2016)], we have characterized experimentally the generation by
this mechanism of a daughter wave, whose amplitude saturates due to the viscous
dissipation. Here, we show experimentally the generation of a daughter wave
verifying the resonant conditions, but not the dispersion relation.} By
modeling the response of the free surface at the lowest nonlinear order, we
explain this observation as a forced interaction. {The bandwidth of the linear
transfer function of the free surface is indeed increased by the significant
viscous dissipation.} The observation of free surface excitations not following
the linear dispersion relation then becomes possible. This forced three-wave
interaction mechanism could have important consequences for wave turbulence in
experimental or natural systems with non negligible dissipation.
