How Does the Average Frequency (w1+w2)/2 Affect Undamped Forced Vibrations?

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aritra
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as we know ,the equation to the undamped forced vibration is
x=Asin{(w1+w2)/2}sin{(w1-w2)/2},the symbols have their usual meaning..but i can't understand how (w1+w2)/2 comes in picture in the phasor diagram...also its significance
 
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