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Question

One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance x0 from the block. The spring is then compressed by 2x0 and released. The time taken to strike the wall is

  1. fraction numerator 1 over denominator 6 end fraction pi square root of fraction numerator k over denominator m end fraction end root    
  2. square root of fraction numerator k over denominator m end fraction end root    
  3. fraction numerator 2 pi over denominator 3 end fraction square root of fraction numerator m over denominator k end fraction end root    
  4. fraction numerator pi over denominator 4 end fraction square root of fraction numerator k over denominator m end fraction end root    

The correct answer is: fraction numerator 2 pi over denominator 3 end fraction square root of fraction numerator m over denominator k end fraction end root


    The total time from A to C
    = tAC = tAB + tBC = (T/4) + tBC
    where T = time period of oscillation of spring -mass system
    tBC can be obtained from, BC = AB sin (2p/T) tBC
    putting fraction numerator B C over denominator A B end fraction equals fraction numerator 1 over denominator 2 end fractionwe obtain t subscript B C end subscript equals fraction numerator T over denominator 12 end fraction
    Þ tAC = fraction numerator T over denominator 4 end fraction plus fraction numerator T over denominator 12 end fraction=fraction numerator 2 pi over denominator 3 end fraction square root of fraction numerator m over denominator k end fraction end root.

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