Three simple harmonic motion in the same direction having the same amplitude and same period are sus

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Three simple harmonic motion in the same direction having the same amplitude and same period are suspended. If each differ in phase from the next by 45o, then

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From superposition priciple y = y1 + y2 + y3 = a sin &#969;t + a sin (&#969;t + 45o) + a sin (&#969;t + 90o) = a[ sin &#969;t + sin (&#969;t + 90o)] + a sin (&#969; + 45o) = 2a sin (&#969;t + 45o) cos 45o + a sin (&#969;t + 45o) = (&#8730;2 + 1) a sin (&#969;t + 45o) = A sin (&#969;t + 45o) Therefore, resultant motion is simple harmonic of amplitude A = (&#8730;2 + 1)a and which differ in phase by 45o relative to the first. Energy in SHM &#8733; (amplitude)2 [E = mA2 &#969;2] &#8756; = = (&#8730;2 + 1)2 = (3 + 2&#8730;2) &#8756; Eresultant = (3 + 2&#8730;2) Esingle

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