Mechanics problem about simple harmonic motion

[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).

 

[Doc Al]

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

 

[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...

 

[Doc Al]

Well, I guess F=10x-10

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.

Doesn't there has to be some differential equation involved?

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?

 

[gipc]

I assume you know the solution by heart or can look it up

Unfortunately, you assume wrong

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

 

[Doc Al]

http://en.wikipedia.org/wiki/Simple_harmonic_motion"