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:
[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

 

[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 [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.

 

[nlightner]

Hello, thank you for your question. I understand your confusion with the different symbols and equations for simple harmonic motion. Let me try to clarify this for you.

Firstly, the equation \omega = \sqrt{\frac{k}{m}} is the correct equation for angular frequency in simple harmonic motion. As you said, it represents the relationship between the spring constant (k) and the mass (m) of the object undergoing simple harmonic motion. This equation tells us the frequency at which the object will oscillate back and forth.

Now, in the book you mentioned, they have used the symbol "p" instead of "\omega" to represent angular frequency. This is not entirely incorrect, as "p" can also represent angular frequency, but it is not the standard symbol used in most textbooks. The symbol "p" is more commonly used to represent linear momentum, which is a different concept in physics.

Regarding the confusion with the equation x = x_{m} sin(pt + \phi), this is a standard equation used to represent the displacement (x) of an object undergoing simple harmonic motion. The "p" in this equation represents the angular frequency, which is why it is multiplied by time (t) to give us the argument of the sine function.

In summary, both the equations you mentioned are essentially the same, just represented with different symbols. The book you are using may have used non-standard symbols, which can be confusing. It is always best to refer to standard textbooks or resources when studying for exams.

I hope this explanation helps clear up your confusion. If you have any further questions, please don't hesitate to ask. Best of luck in your studies!