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The sinusoidal nature of pendulum motion

From Physics Classroom:

A displacement to the right of the equilibrium position would be regarded as a positive displacement; and a displacement to the left would be regarded as a negative displacement. Using this reference frame, the equilibrium position would be regarded as the zero position. And suppose that we constructed a plot showing the variation in position with respect to time. The resulting position vs. time plot is shown below. Similar to what was observed for the mass on a spring, the position of the pendulum bob (measured along the arc relative to its rest position) is a function of the sine of the time.

In the video above, what we are seeing is the alignment of the differing sine waves, one for each pendulum. They do not stay aligned for long because the length of string they are attached to gives them different periods (the amount of time it takes to return to the starting position). When the sine waves do constructively match, we see some sort of pattern. When they destructively match, we see no pattern.

Due to the different periods (due to the length of string), we see different patterns at different times, until, given a long enough period, the waves sync back to how they were first released.