Question

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

Answer 1

\[ F = \frac{dU}{dx} \hat{x} \]
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.)

Answer 2

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

Answer 3

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

Answer 4

Making sense?

Answer 5

Sorry, I don't get it :|

Answer 6

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