Summation of codirectional oscillations

Let us begin with the simplest case summation of two oscillations with the same frequencies  

Let us analyze the result. The phase difference of the summing oscillation remains constant at any time instance it is the difference of the initial phases, i.e.. 

As can be seen from expression (2.3.1), the resulting amplitude depends on the phase difference of the summed oscillation, hi particular, if the phase difference A(p satisfies the condition 

The modulus is used here because the amplitude must be positive. 

It is clearly seen that oscillation will not take place at all in this case having equal amplitudes and oscillating in antiphase, they have cancelled each other out. 

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