The potential energy of the body is given by: U(x) = 3cosh(x). Find the corresponding force F(x) as a function of the coordinate x. Draw its plot

Question

The potential energy of the body is given by: U(x) = 3cosh(x). Find the corresponding force F(x) as a function of the coordinate x. Draw its plot

Answer 1

F(x) = -dU/dx in the +x direction (If F is negative, it points the other way.

The - derivative of cosh(x) = -sinh(x) or (e^-x- e^x)/2

You can plot that on Desmos.com graphing calculator. It looks like a steeper version of y = -x³

U(x) looks like a U, so it makes sense that it's slope is positive on the right of the origin and negative to the left of the origin (0 at the origin) and the F(x) is the opposite (always pointing to the origin - conservatively like a marble in a bowl)