Diaphragm type controlling the time period of structure

Why is the type of diaphragm influencing the time period of the structure? Time period of structure is related to the mass and stiffness of the lateral force resisting system. Where does the diaphragm action coming into play? I considered two different models: one with rigid diaphragm and another with semi rigid diaphragm. Model with rigid diaphragm gives lower time period. Can anyone please provide some insights on this?

Also how can we look at modal participation ratios for different modes to determine if it is just local mode or not?