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A particle of mass m is attached to three identical springs A, B and C each of force constant k a shown in figure. If the particle of mass m is pushed slightly against the spring A and released then the time period of oscillations is

  1. 2 pi square root of fraction numerator 2 m over denominator k end fraction end root    
  2. 2 pi square root of fraction numerator m over denominator 2 k end fraction end root    
  3. 2 pi square root of fraction numerator m over denominator k end fraction end root    
  4. 2 pi square root of fraction numerator m over denominator 3 k end fraction end root    

The correct answer is: 2 pi square root of fraction numerator m over denominator 2 k end fraction end root


    When the particle of mass m at O is pushed by y in the direction of A The spring A will be compressed by y while spring B and C will be stretched by y to the power of ´ end exponent equals y cos invisible function application 4 5 degree. So that the total restoring force on the mass m along OA.

    F subscript n e t end subscript equals F subscript A end subscript plus F subscript B end subscript cos invisible function application 4 5 degree plus F subscript C end subscript cos invisible function application 4 5 degree
    equals k y plus 2 k y to the power of ´ end exponent cos invisible function application 4 5 degree equals k y plus 2 k left parenthesis y cos invisible function application 4 5 degree right parenthesis cos invisible function application 4 5 degree equals 2 k y
    Also F subscript n e t end subscript equals k to the power of ´ end exponent y Þ k to the power of ´ end exponent y equals 2 k yÞ k to the power of ´ end exponent equals 2 k
    T equals 2 pi square root of fraction numerator m over denominator k to the power of ´ end exponent end fraction end root equals 2 pi square root of fraction numerator m over denominator 2 k end fraction end root

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