Fully coupled aero-hydro-control-elastic codes are being developed to cope with the new modelling challenges presented by floating wind turbines, but there is also a place for more efficient methods of analysis. One option is linearisation and analysis in the frequency domain. For this to be an effective method, the non-linearities in the system must be well understood. The present study focusses on understanding the dynamic response of the rotor to the overall platform motion, as would arise from wave loading, by using a simple model of a floating wind turbine with a rigid tower and flexible rotor (represented by hinged rigid blades). First, an equation of motion of the blade is derived and an approximate solution for the blade response is found using the perturbation method. Secondly, the full non-linear solution is found by time- domain simulation. The response is found to be linear at lower platform pitching frequencies, becoming non-linear at higher frequencies, with the approximate solution giving good results for weakly non-linear behaviour. Higher rotor speeds have a stabilising effect on the response. In the context of typical floating turbine parameters, it is concluded that the blade flapwise response is likely to be linear.