## Abhisar one year ago A particle moves in a potential region given by $$\sf U=8x^2-4x+400$$ J. Its state of equilibrium will be

1. Abhisar

@Michele_Laino

2. Michele_Laino

we have to request that the subsequent condition holds: $\Large \frac{{\partial U}}{{\partial x}} = 0$

3. Abhisar

Oh, so you mean we have to solve the equation for u=0?

4. Michele_Laino

not for U=0, its first derivative with respect to x has to be equal to zero, since, in a field of force coming from a potential, the relationship between force and potential energy is: $\Large {\mathbf{F}} = - \nabla U$

5. Abhisar

Oh, one min....

6. Abhisar

Ok, yes. Thanks a bunch c:

7. Michele_Laino

thus we get the subsequent condition: $\Large {x_0} = \frac{1}{4}$ as equilibrium position

8. Michele_Laino

:)

9. Abhisar

Yes... c:

10. Michele_Laino

:)

11. UnkleRhaukus

now, the sign of the second derivative at this point, will determine whether this equilibrium point is stable or unstable

12. Abhisar

Oh I see, thanks for the info Felix c: