A point mass is placed on a surface at (x,y) which is undulating. That is, the surface’s transverse or vertical displacement w(x,y,t) is moving as  a function of time. What is the vertical or transverse force acting on that point mass? For example, is the force proportional to a shearing motion, as in (d3w/dx3)2+(d3w/dy3)2, or is it proportional to a moment, as in (d2w/dx2)2+(d2w/dy2)2, or is proportional to a slope (gradient), as in (dw/dx)2+(dw/dy)2 or something else?

Thanks.