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Oscillations from Potential

  1. Oct 6, 2009 #1
    1. U(x)=U0(x/a)^1000000
    Find the period for a mass m, if it has total energy E


    2. E=U+K




    3. dE/dt=0=v[mdv/dt+dU/dx]

    Im really stuck on this one, im not sure what to do at all talked to my proffessor he says just to re-read the chapter but if im honest ive always been one to learn through examples which he hasnt given us, any clues would be most appreciated!
     
  2. jcsd
  3. Oct 7, 2009 #2

    berkeman

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    Staff: Mentor



    Is this a spring and mass problem, or a pendulum problem or what? Please post more details and the relevant equations in more detail, and show us how you have tried to start the solution...
     
  4. Oct 7, 2009 #3
    its a SHM probelm, well i tried
    -dU/dx=F(x)
    F(x)=m(d^2x/dt^2)
    then i think im meant to guess a value for x(t) but im not really sure/
     
  5. Oct 7, 2009 #4
    First I suggest that you express the potential energy as:

    [tex]U(x)=\frac{U_0}{a^{k+1}}x^{k+1}[/tex] where in our case [tex]k+1=1000000[/tex]

    Use the following theorem:

    [tex]F(x)=-U'(x)[/tex]

    And from there all that remains is to solve a tricky differential equation. I'm trying it myself, it looks interesting.
     
  6. Oct 7, 2009 #5
    If E=U+K
    E=((U0x^K+1)/a^k+1)+0.5(m)(dx/dt)^2
    rearrange
    dx/dt=(2/m(E-U0x^K+1)/a^k+1))^0.5
    is this the right way about, im not sure how to do this integral.
     
  7. Oct 8, 2009 #6
    This system doesn't look to be SHM.
     
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