Mechanics problem about simple harmonic motion

AI Thread Summary
The discussion revolves around calculating the period of small oscillations and the spring constant for a mass connected to a spring, given the potential energy function U(x) = 5x^2 - 10x + 12. The force is derived from the potential energy, leading to F = -dU/dx = 10x - 10, indicating the spring constant can be identified from this equation. Participants clarify that while a differential equation is involved, it follows the standard form for simple harmonic motion. The user expresses uncertainty about the necessary mathematical steps to find the period, indicating a need for guidance in solving the problem. The conversation emphasizes the importance of understanding the relationship between force, potential energy, and harmonic motion.
gipc
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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).
 
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What's the spring constant? Hint: How do you find the force as a function of x?
 
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...
 
gipc said:
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?
 
Doc Al said:
I assume you know the solution by heart or can look it up

Unfortunately, you assume wrong :rolleyes:

Perhaps someone can show me the mathematical steps needed to solve this?
 
http://en.wikipedia.org/wiki/Simple_harmonic_motion"
 
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