It is demonstrated that a constant frequency measurement of a purely real property that varies due to a change in some state variable (e.g., pressure, volume, or temperature) with Lime will show a dynamically induced loss that is not present when the variable is held constant. This conclusion is demonstrated through both generalized arguments and by examining some specific functional forms of time evolution equations, including one that resembles a glass transition. Our results show that techniques such as dielectric thermal analysis, dynamic mechanical thermal analysis, and modulated differential scanning calorimeter, which perform measurements of complex quantities while scanning in temperature, may have some serious problems. Therefore, results obtained from these techniques should be examined carefully before using them to prove or disprove theoretical model predictions, especially in the neighborhood of a phase transition.