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A particle moves such that its position from origin is given by ( x =2+3 ^2 t ). Choose CORRECT statement(s) about its motion :- (A) Particle performs S.H.M. of amplitude ( 3 2 m ) and frequency ( ) (B) Particle performs oscillations but no S.H.M. (C) Particle performs S.H.M. about mean position at (x= 7 2 m ) (D) Particle performs oscillations of amplitude 3 m

Options

  1. AB,D
  2. BA,C
  3. CA,C,D
  4. DNone

Correct answer

D. None

Step-by-step solution

1. Analyzing the Statements: - (A): Particle performs S.H.M. of amplitude (3, m ) and frequency ( ). - False: The amplitude is actually ( 3 2 , m ) (not (3, m )), and frequency is derived from ( (2 t) ) which would be ( 2 2 = ), but the amplitude is incorrect. (B): Particle performs oscillations but no S.H.M. - False: The particle does perform oscillatory motion about a mean position with a periodic nature (but not simple harmonic due to the ( ^2 ) term). (C): Particle performs S.H.M. about mean position at (x=7, m

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