A bead, under the influence of gravity, slides along a frictionless wire whose height is given by the function V (x) (see Fig.). Find an expression for the bead??s horizontal acceleration x. (It can depend on whatever quantities you need it to depend on.) You should find that the result is not the same as the x for a particle moving in one dimension in the potential mgV (x), in which case x = ?gV??. But if you grab hold of the wire, is there any way you can move it so that the bead??s ?x is equal to the x = ?gV?? result due to the one-dimensional potential mgV (x)?

height = l(x)