Physics-
General
Easy

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 xo from the black. The spring is then compressed by  2xo and released. The time taken to strike the wall is

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

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


    The total time from A to C
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell t subscript A C end subscript equals t subscript A B end subscript plus t subscript B C end subscript end cell row cell equals left parenthesis T divided by 4 right parenthesis plus t subscript B C end subscript end cell end table
    Where  T= time period of oscillation of spring mass system
    tBC can be obtained from, B C equals A B sin invisible function application left parenthesis 2 pi divided by T right parenthesis t subscript B C end subscript
    Putting fraction numerator B C over denominator A B end fraction equals 1 half text  we obtain  end text t subscript B C end subscript equals T over 12
    not stretchy rightwards double arrow t subscript A C end subscript equals T over 4 plus T over 12 equals fraction numerator 2 pi over denominator 3 end fraction square root of m over k end root

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