Abstract: The sampling theorem in signal and system theory,demands sample the time zone limitlessly widely, amount of data sampled is many limitlessly. This is a kind of idealized situation. It can only be limited to sample the width of time zone and amount of data sampled actually. Therefore, it is difficult for the sampling theorem to use and explore the law that the physical quantity evolved with time. The need of combining the physics experiment and studying, we propose the revising sampling theorem for utilizing limited sampled data and revising sampling theorem, which can catch the evolution law of cycle physical quantity accurately. The method is, fetch the time in- terval T8 as small as possible, fetch the number of times of observation as large as possible, to observe cycle physi- cal quantity N times. We analyze the sampled data and find out cycle T of the physical quantity, adjust T and N by observing repeatedly,make NT8/T equal to the integer. We calculate spectral Xs（f） which samples the data, utilize the revising sampling theorem and X （f）, and get spectral X （f） of cycle physical quantity fast. According to X（f） , we rebuild law that the cycle physical quantity evolved with time. As an example, large tilt angle simple pendulum as the research object, we show the method and process of cycle phenomenon law.

Key words: cycle phenomenon, physical quantities, spectrum, variation law