Quick question about Simple Harmonic Motion

[Dr. Mirrage]

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:
\omega = \sqrt{\frac{k}{m}}

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:
p^{2} = \frac{k}{m}
which is basically the exact same thing except they have "p" instead of "\omega" which is "momentum" instead of "angular frequency", right?
Furthermore, they proceed to cause more confusion for me by writing things like:
x = x_{m} sin(pt + \phi)
shouldn't it be "\omega t" 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: Period = T = \frac{2\pi}{\omega}
I know that equation is correct, and they definitely used the character "omega" for "angular frequency"..

I've then been trying to show that p = \sqrt{\frac{k}{m}} = \omega But have so far been unsuccessful.
I would be very grateful if someone could help me sort this out. Thanks

 

[diazona]

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

Anyway, the equations you've got there only make sense if p is angular frequency. So I would just assume that p = \omega, 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 \omega, 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.