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anonymous

  • 4 years ago

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

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  1. JamesJ
    • 4 years ago
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    \[ F = \frac{dU}{dx} \hat{x} \] 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
    • 4 years ago
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    Hence, for instance, for x < pi, the force F is the zero vector because the derivative of the potential 1 is zero.

  3. JamesJ
    • 4 years ago
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    And I should have included a minus sign. \[ F = - \frac{dU}{dx} \hat{x} \]

  4. JamesJ
    • 4 years ago
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    Making sense?

  5. anonymous
    • 4 years ago
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    Sorry, I don't get it :|

  6. JamesJ
    • 4 years ago
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    What is the function U(x)? Not its mathematical definition. What is its physical interpretation?

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