why two objects transfer energy between each other with maximum efficiency only when they have the same resonant frequency

Two objects transfer energy between each other with maximum efficiency only when they have the same resonant frequency because resonance occurs when the natural vibration frequency of one object matches the natural vibration frequency of the other object. When this happens, the amplitude of the vibrations of both objects increases, causing a strong transfer of energy between them.

If the frequencies of the two objects are not the same, the transfer of energy will be less efficient because the vibrations of the two objects will not be in sync, and some of the energy will be lost as heat or sound. Therefore, for maximum efficiency, it is necessary for the two objects to have the same resonant frequency.