A particle starts executing simple harmonic motion ( SHM ) of amplitude a and total energy E . At any instant, its kinetic energy is 3 E 4 , then its displacement y is given by:

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E = 1 2 K a 2 3 E 4 = 1 2 K a 2 - y 2 v 3 4 × 1 2 K a 2 = 1 2 K a 2 - y 2 y 2 = a 2 - 3 a 2 4 y = a 2

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