The purpose of this study is to experimentally examine the oscillation frequencies of liquid slugs in multi-turn micro pulsating heat pipes (MPHPs) and to perform a theoretical study for better understanding of the experimental results. A series of experiments on silicon-based MPHPs with different overall lengths of 40, 50, and 60 mm are performed at different heat inputs in a bottom-heating mode. Ethanol is used as a working fluid at a filling ratio of 55%. From a spectral analysis on flow visualization data, dominant frequencies of the MPHPs are identified for each experimental condition. To theoretically estimate the dominant frequencies, a 'non-adiabatic' vapor spring liquid mass model is proposed: The spring action of a vapor plug is linked not only to a volume variation but also to a mass variation of a non-adiabatic vapor plug via phase change processes. A distinguishing feature of this model is that it is capable of handling the mass variation of a vapor plug due to phase change processes. Based on the model, a set of parameters related to the oscillation frequency is explicitly determined: the number of turns, channel length, filling ratio, liquid density, vapor pressure and specific heat ratio. A closed-form correlation of the oscillation frequency is proposed and found to be accurate in predicting the experimental data to within 15%. It is also shown that the oscillation frequency is over-predicted by more than 100% of the experimental data when the spring-mass model is used without including the mass variation due to phase change processes.