Abstract: The work -energy theorem for systems with time related force field possessing potential and other forces has more powerful application value than the ordinary work-energy theorem.This paper plans to introduce the former and apply it to judge whether the mechanical energy relative to different reference systems is conservative for two simple systems：a particle in the gravity field and a light spring oscillator with one end fixed in the moving compartment.

Key words: time related field, work - energy theorem, theorem of mechanical energy conservation, gravity field, light spring oscillator