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Most commercial large wind turbines use blade pitch action to mitigate structural loads in high wind velocity conditions. In this paper, we study the linearized dynamics of the map from blade pitch to tower top fore-aft deflection in horizontal-axis wind turbines. We show that the mass and stiffness distribution of the blades at certain operating conditions determine the presence (or absence) of a right half-plane zero in the transfer function of interest. We conclude that blade design can impose constraints on the achievable tower fore-aft oscillation mitigation through collective blade pitch control. Consequences of this result to wind turbine design are discussed.