What Physical Situation is Governed by the Standard SHO Potential?

[ehrenfest]

Homework Statement

My QM book says that the standard SHO potential is $$m \omega^2 x^2/2$$. Can someone give me an example of a physical situation that is governed by this potential. It seems rather out of nowhere to me...

Homework Equations

The Attempt at a Solution

 

[cristo]

Any situation that is governed by Hookes Law: f=-kx, will have a potential V=kx^2/2

 

[ehrenfest]

Yes but when is k = m \omega x? I guess \omega = g works, but
omega is usually an angle.

 

[G01]

You are probably thinking of the oscillator potential energy using the formula:

$$V=1/2kx^2$$

Remember that Omega is the angular frequency of the oscillation. Also, remember that for an oscillator obeying Hooke's Law the angular frequency is:

$$\omega = \sqrt{k/m}$$

If you solve this for k, you should see where the m*omega^2 is coming from in the book's expression for the potential energy.