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Elastic Potential Energy

  1. Apr 11, 2008 #1
    1. The problem statement, all variables and given/known data
    A simple harmonic oscillator has a total energy E.
    a) Determine the kinetic and potential energies when the displacement is one half the amplitude.
    b) For what value of the displacement does the kinetic energy equal the potential energy?


    2. Relevant equations
    PEs= 1/2Kx^2
    KE = 1/2mv^2


    3. The attempt at a solution

    I actually have the solution given to me, but I don't understand some of the steps.

    We know that x=A/2, so:
    PEs= 1/2K(A/2) which we can expand to K/8A^2

    Then they say that: K/8A^2 = K/8(2E/K) and this is the part I'm confused about. Why does A^2=2E/K?

    Thanks!
     
  2. jcsd
  3. Apr 11, 2008 #2

    Doc Al

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    Staff: Mentor

    Hint: Express the total energy (E) in terms of amplitude. (At what point is the energy purely PE?)
     
  4. Apr 11, 2008 #3
    When x=0?
     
  5. Apr 11, 2008 #4

    Doc Al

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    Staff: Mentor

    What's the PE when x = 0?
     
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