Question: Demonstrate that when two harmonic oscillations are added, the time-averaged energy of the resultant oscillation is equal to the sum of the energies of the

Demonstrate that when two harmonic oscillations are added, the time-averaged energy of the resultant oscillation is equal to the sum of the energies of the constituent oscillations, if both of them
(a) Have the same direction and are incoherent, and all the values of the phase difference between the oscillations are equally probable;
(b) Are mutually perpendicular, have the same frequency and an arbitrary phase difference.

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a In this case the net vibration is given by x a cos w t a cos w t 8 where ... View full answer

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