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Homework Help: Quick question about Simple Harmonic Motion

  1. Jul 9, 2009 #1
    I'm going to dispense with the provided template for this, I hope no one minds.

    I always understood that for simple harmonic motion there was this equation:
    [tex]\omega = \sqrt{\frac{k}{m}}[/tex]

    However, I recently got a book that helps you study for the Physics GRE (Graduate Record Examination).
    There is a quick review in there covering all the material that you should learn as an undergraduate physics student. However, it just made me confused when I got to this part about Simple Harmonic Motion, because they write the above equation as:
    [tex]p^{2} = \frac{k}{m}[/tex]
    which is basically the exact same thing except they have "p" instead of "[itex]\omega[/itex]" which is "momentum" instead of "angular frequency", right?
    Furthermore, they proceed to cause more confusion for me by writing things like:
    [tex]x = x_{m} sin(pt + \phi)[/tex]
    shouldn't it be "[itex]\omega t[/itex]" instead of "pt"?

    So I was thinking maybe they just use the character "p" for "angular frequency", but then the very next equation I see in the book is: [itex]Period = T = \frac{2\pi}{\omega}[/itex]
    I know that equation is correct, and they definitely used the character "omega" for "angular frequency"..

    I've then been trying to show that [itex]p = \sqrt{\frac{k}{m}} = \omega[/itex] But have so far been unsuccessful.
    I would be very grateful if someone could help me sort this out. Thanks
  2. jcsd
  3. Jul 9, 2009 #2


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    Homework Helper

    If the template doesn't apply, it's probably not a homework question, is it? :wink:

    Anyway, the equations you've got there only make sense if p is angular frequency. So I would just assume that [itex]p = \omega[/itex], i.e. that they are using both letters for the same physical quantity. It's bad notation, but what can you do...

    Actually you could rewrite the formulas to use [itex]\omega[/itex], so they look right to you. Making your own formula sheet (even if you can't use it on the test) is a good practice in general.
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