# Mechanics problem about simple harmonic motion

1. Aug 29, 2010

### gipc

Hi,
Can anyone help me with this question?

The potential energy of mass (m=6KG) that is connected to a spring is given by:
U(x) = 5x ^ 2 -10x +12

Find the period of the small fluctuations around the equilibrium point (in seconds).

2. Aug 29, 2010

### Staff: Mentor

What's the spring constant? Hint: How do you find the force as a function of x?

3. Aug 29, 2010

### gipc

Well, I guess F=10x-10

and i've thought about doing

10x-10=-kx
but i don't think it will suffice.

Doesn't there has to be some differential equation involved? I'm really scared of those...

4. Aug 29, 2010

### Staff: Mentor

Almost. F = - dU/dx. (You just forgot the minus sign.)

The constant just tells you that the equilibrium position is not at x = 0. You can read off the spring constant from that force equation.
Sure, but it's the same differential equation as for any simple harmonic motion. I assume you know the solution by heart or can look it up. If you knew the spring constant and the mass, could you find the period?

5. Aug 29, 2010

### gipc

Unfortunately, you assume wrong :uhh:

Perhaps someone can show me the mathematical steps needed to solve this?

6. Aug 29, 2010

### Staff: Mentor

http://en.wikipedia.org/wiki/Simple_harmonic_motion" [Broken]

Last edited by a moderator: May 4, 2017