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Determine the oscillation period

  1. Mar 7, 2014 #1
    1. The problem statement, all variables and given/known data

    Determine the oscillation period, as a function of energy E, when a particle of mass m moves in a field with potential energy [itex]V(x)=-V_0/cosh^2(\alpha x)[/itex], for [itex]-V_0 < E < 0[/itex] with Vo positive.

    (a) First show that, with s=sinh (α x) and determining the appropriate smax ,the period satisfies

    [itex]T=\frac{2\sqrt{2m}}{\alpha\sqrt{E}}\int_{0}^{S_{max}}\frac{ds}{\sqrt{s^2}+\frac{E+U_o}{E}}[/itex]

    2. Relevant equations
    Not sure where to start. My text-book is of no help when it comes to this question


    3. The attempt at a solution
    I am not sure where to start....

    Can someone help me with this one. thanks!
     
  2. jcsd
  3. Mar 7, 2014 #2

    TSny

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    Show some attempt. You know you need to use energy ideas. What can you say about the relation between kinetic energy, potential energy, and total energy E?
     
  4. Mar 7, 2014 #3
    T + v = e.... Don't see what the would do?
     
  5. Mar 7, 2014 #4

    TSny

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    Suppose you could express the speed v as a function of x. Note v = dx/dt. So, you would have dx/dt = some function of x.
     
  6. Mar 7, 2014 #5
    Ya I get that, i just don't know how to get smax
     
  7. Mar 7, 2014 #6

    TSny

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    What can you say about the value of the potential energy V(x) when s = smax?
     
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