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Physics II forgotten equation (oscillations)

  1. Sep 12, 2011 #1
    I am reviewing for a test on oscillations and I have no clue how I derived a formula I used for my homework.

    Could anyone help me figure out where the equation [itex]v=w{\sqrt{A^2x^2}}[/itex] comes from? Thank you.
     
    Last edited: Sep 12, 2011
  2. jcsd
  3. Sep 12, 2011 #2

    vela

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    That equation can't be correct. The units on the RHS work out to be length2/time.
     
  4. Sep 12, 2011 #3
    I actually just found the equation in the book, it comes from the conservations of energy formula. I don't understand how it can work for the same reason you listed, that's why I am confused. And I'm 100% sure I am copying it down correctly.

    It is derived from:

    [itex]\frac{1}{2}mv_x^2 + \frac{1}{2}kx^2=\frac{1}{2}kA^2[/itex]

    [itex]mv_x^2 + kx^2=kA^2[/itex]
     
  5. Sep 12, 2011 #4

    vela

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    Try solving for the velocity.
     
  6. Sep 12, 2011 #5
    You get [itex]v={\sqrt{{\frac{k}{m}}A^2x^2}}[/itex] which is equivolaent to [itex]v=w{\sqrt{A^2x^2}}[/itex].
     
  7. Sep 12, 2011 #6

    vela

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    No, you don't. How'd you get that?
     
  8. Sep 12, 2011 #7
    [itex]mv_x^2 + kx^2=kA^2[/itex]

    Sorry, I'm not gonna use latex for this so I can do it faster.

    mv^2=kA^2-kx^2

    v^2=(kA^2-kx^2)/m

    v^2= (k/m)(A^2-x^2)

    v=sqrt((w^2)(A^2-x^2))

    v=w(sqrt(A^2-x^2))

    I think that was actually beneficial for me typing that out lol.
     
  9. Sep 12, 2011 #8

    vela

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    Yup, that's the equation I think you were looking for.
     
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