One-Dimensional Gradient Motion

Consider a particle moving along the x-axis in a "potential well" given by a potential function f(x). The potential gives rise to a force on the particle, with the force determined by the negative gradient of the potential function, -grad f(x). (We have written -grad f(x) instead of -f'(x) to emphasize that we want to think of the force as being a one dimensional vector field.)

For the remainder of the lab, suppose f(x)=-cos(x).

Question #1:

Sketch the force field for this potential function on the x-axis for x in the interval [-2 Pi,2 Pi]. At what points is the force 0?

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Bob Thurman;thurman@geom.umn.edu>

Last modified: Tue Apr 2 13:46:36 1996