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A particle of mass m moves in a one dimensional potential

  1. Apr 27, 2015 #1
    1.The problem, statement, all variables and given/known data

    A particle of mass m moves in a one dimensional potential U(x)=A|x|3, where A is a constant. The time period depends on the total energy E according to the relation T=E-1/k
    Then find the value of k.

    2. Relevant equations


    V=dx/dt
    E=kinetic energy + U
    F=-dU/dx
    3. The attempt at a solution

    ##E=\frac{1}{2}mv^2+a|x|^n##
    ##v=\sqrt{\frac{2}{m}(E-a|x|^n)}##
    ##dt=\frac{dx}{v}##
    Integrating LHS, I can get the time period. But when integrating RHS, how do I find the limits?
     
  2. jcsd
  3. Apr 28, 2015 #2

    ehild

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    Homework Helper
    Gold Member

    The particle moves between the turning points, where its velocity becomes zero, that is, the potential energy is equal to the total energy E.
     
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