Calculating Potential Energy from Force for Non-Linear Systems

AI Thread Summary
To calculate potential energy from the force given by F(x) = αx - βx^3, the relationship -dV(x)/dx = F(x) is used. The limits of integration can be chosen freely, as the integration constant does not influence the force. Setting the potential energy to zero at x = 0 is acceptable and will not affect the physical outcomes. This choice simplifies calculations while maintaining the integrity of the system's physics. The discussion confirms that selecting a zero-level for potential energy is a matter of convenience.
RubroCP
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Homework Statement
##F(x)=\alpha x-\beta x^3##
Relevant Equations
##-\frac{\mathrm{d}V(x)}{\mathrm{d}x}=F(x)##
If I have a force that behaves according to the formula ##F(x)=\alpha x-\beta x^3##, how can I get the potential energy from it? I know that:
$$-\frac{\mathrm{d}V(x)}{\mathrm{d}x}=F(x),$$
but what about the limits of the integration?
 
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The integration constant is not physical as it does not affect the force. It is up to you to choose the zero-level of the potential.
 
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Orodruin said:
The integration constant is not physical as it does not affect the force. It is up to you to choose the zero-level of the potential.
So can I say without loss of generality that for x = 0 the potential is also null?
 
Yes, this will not affect the physics.
 
Orodruin said:
Yes, this will not affect the physics.
Thanks!
 
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