9.2.1 Phase Relationship

Phase relationship is a concept unique to periodic repetitive patterns.

Take the phases of the Moon as an example: It is a repetitive pattern with a period of one month, with fanciful names for different phases such as the New Moon, the Crescent, the Gibbous and the Full Moon.

In Mathematics, instead of words, we simply denote the phase with a number between 0° and 360°, or between 0 radian and 2π radians. (As usual, 360° or 2π radians represent one full complete cycle.)

Now we can talk about phase relationships. Suppose we have two pendulums of the same period, but released one after another so that one is always “ahead” of the other. The lead or lag of one oscillation over the other is called the phase difference.

If the phase difference between two oscillations is zero, they are said to be in-phase.

If the phase difference between two oscillations is 180° or π radian, they are said to be completely out of phase, or in antiphase.

If the phase difference between two oscillations is 90° or π/2 radian, they are said to be a quarter-cycle out of phase.

If we line up many oscillations, each succeeding one slightly lagging the preceding one, what are we going to get?

Demonstration

Human Oscillator

Concept Test

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