## anonymous 4 years ago Derive the force for the following intervals U(x) = 1, -∞ < x < -π |x|, -π ≤ x ≤ π sin (x), x > π

1. JamesJ

$F = \frac{dU}{dx} \hat{x}$ So just calculate and notice there will be points where the force is not defined because the derivative is not defined. (Or if you know Dirac delta functions, should be written in terms of them.)

2. JamesJ

Hence, for instance, for x < pi, the force F is the zero vector because the derivative of the potential 1 is zero.

3. JamesJ

And I should have included a minus sign. $F = - \frac{dU}{dx} \hat{x}$

4. JamesJ

Making sense?

5. anonymous

Sorry, I don't get it :|

6. JamesJ

What is the function U(x)? Not its mathematical definition. What is its physical interpretation?