Mechanics problem about simple harmonic motion

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Homework Help Overview

The discussion revolves around a mechanics problem related to simple harmonic motion, specifically focusing on the potential energy of a mass connected to a spring and the determination of the period of small fluctuations around the equilibrium point.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between potential energy and force, with some attempting to derive the spring constant and questioning the need for a differential equation. Others express uncertainty about the mathematical steps required to find the period.

Discussion Status

The discussion is ongoing, with participants providing hints and guidance regarding the force equation and the spring constant. There is a recognition of the need for further mathematical exploration, but no consensus has been reached on the approach to take.

Contextual Notes

Participants express concerns about the complexity of differential equations and the assumptions regarding the equilibrium position. There is also a mention of external resources, indicating a search for additional information.

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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