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Three simple harmonic motions in the same direction having the same amplitude \( a \) and same period are superposed. If each differs in phase from the next by \( 45^{\circ} \), then choose the correct statement.
(a) The resultant amplitude is \( (1+\sqrt{2}) a \).
(b) The phase of the resultant motion relative to the first is \( 90^{\circ} \).
(c) The energy associated with the resulting motion is \( (3-2 \sqrt{2}) \) times the energy associated with any single motion.
(d) The resulting motion is not simple harmonic.
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