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.