Theories are developed to evaluate Larmor frequency shifts, derived from geometric phases, in experiments to measure electric dipole moments (EDMs) of trapped, atoms, molecules and neutrons. A part of these shifts is proportional to the applied electric field and can be interpreted falsely as an electric dipole moment. A comparison is made between our theoretical predictions for these shifts and some results from our recent experiments, which shows agreement to within the experimental errors of 15 %. The comparison also demonstrates that some trapped particle EDM experiments have reached the sensitivity where stringent precautions are needed to minimise and control such false EDMs. Computer simulations of these processes are also described. They give good agreement with the analytical results and they extend the study by investigating the influence of varying surface reflection laws in the hard walled traps considered. They also explore the possibility to suppress such false EDMs by introducing collisions with buffer gas particles. Some analytic results for frequency shifts proportional to the square of the E-field are also given and there are results for the averaging of the B-field in the absence of an E-field.