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  1. Though the example of a pendulum is a special case of periodic function because it is executing simple harmonic motion, the difference lies in how the motion is expressed mathematically.[1]
  2. If the periodic function can be represented by a sine curve, then the motion is said to be simple harmonic motion, like a weight on spring oscillating, a swing, etc.[1]
  3. That repetitive motion is the same idea that’s reflected in the steady pattern of a periodic function.[2]
  4. A periodic function is a function that repeats its values at regular intervals, for example, the trigonometric functions, which repeat at intervals of 2π radians.[3]
  5. A simple example of a periodic function is the function f {\displaystyle f} that gives the "fractional part" of its argument.[3]
  6. A possible way out is to define a periodic function on a bounded but periodic domain.[3]
  7. In the graph below is shown a periodic function with two cycles as an example.[4]
  8. Hence, Graph 2 does not represent a periodic function.[5]
  9. The applet below dynamically depicts what it means for a function to be classified as a periodic function.[6]
  10. Periodic Function A function which has a graph that repeats itself identically over and over as it is followed from left to right.[7]
  11. The theory of almost-periodic functions was initiated by H. Bohr, who developed the notion of a uniformly almost-periodic function in his study of Dirichlet series.[8]
  12. A non-periodic function does not remain self-similar for all integer multiples of its period.[9]
  13. A decaying exponential is an example of a non-periodic function.[9]
  14. The period of a periodic function is the smallest P>0 such that this holds.[10]
  15. Creating a visual representation of a periodic function in the form of a graph can help us analyze the properties of the function.[11]
  16. I thought it to be true , as everything about a periodic function repeats itself at regular intervals, and so should it's derivative .[12]
  17. If a function has a repeating pattern like sine or cosine, it is called a periodic function.[13]

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  • [{'LOWER': 'periodic'}, {'LEMMA': 'function'}]