Beating effects between a thermoacoustic source and its mechanical partner-a piston-spring oscillator are numerically predicted and experimentally observed in the free-decay process. Through analyzing the indicator diagram, periodic energy transfer characteristics between a thermoacoustic source and its mechanical partner during the beating oscillation are revealed and analyzed. The oscillation frequency is found to split into two modes intrinsically even when the resonance frequencies are initially tuned to be the same. The patterns and frequencies of the beating oscillations are sensitively affected by the characteristics of acoustic sources. The study sheds light on the underlying mechanisms of beating oscillations occurred in thermoacoustic systems with multiple resonant sub-units.