Energy & Spring Displacement function

AI Thread Summary
The discussion revolves around calculating the energy required to stretch a spring defined by the force equation \vec{F}_{spring} = - (ax + βx^2)\hat{x}. Participants are encouraged to explore the derivation of the energy expression for a linear spring, specifically \vec{F} = -a\vec{x}. There is a focus on understanding the foundational equations and concepts related to spring displacement and energy. The conversation highlights the initial confusion some may have when approaching the problem. Overall, the thread aims to clarify the relationship between force and energy in the context of spring mechanics.
TheWhiteKnyt
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Homework Statement


What would be the energy required to stretch a spring of \vec{F}spring = - (ax+βx^2)\hat{x} where\vec{x} = x*\hat{x}

Homework Equations


[/B]
\vec{A}/|A| = \hat{A}
|\vec{A}| = sqrt(A*A)
A = (A^x)^2 + (A^y)^2

The Attempt at a Solution


[/B]
So far I'm at a loss just getting started.
 
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Hello White, welcome to PF :)

To get started:
Do you know the energy required to stretch a spring of ##\vec F = -a\vec x ## ? How was that expression derived ?
 

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