How do we know a motion is periodic?

How do we know a motion is periodic? Is there a way to mathematically distinguish it from linear motion?


  • A motion which repeats itself after equal intervals of time. For example, a pendulum oscillating, someone on a swing. Even something that is undergoing rotation is under periodic motion.
  • kkanadekkanade Forum Coordinator
    If you plot the position vs time curve for a body and the curve is sinusoidal (i.e. shaped like a sine curve), then you can say that the body is undergoing periodic motion. Linear motion in a single direction will most like have a linear curve when position vs time is plotted (unless it's velocity changes in which case it won't be a straight line with fixed slope, but a curve with varying slopes).
  • Thank you both for the replies!! 🙂

    But @prajputmentioned that rotation is also a periodic motion. How is that motion represented by a sinusoidal curve?

  • kkanadekkanade Forum Coordinator
    Imagine a circle with a diameter drawn on it. Imagine you have a particle on one end of the diameter that moves along the circumference of the circle. If we assume the center of the circle to be the origin and the diameter to be the x-axis, plotting the x-position of the moving particle with respect to time will give a sinusoidal curve. Similarly it's y-position will also give a sinusoidal curve when plotted against time.
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