I can't get started on either I am stuck that's why I posted the problem. I know that you set the first part equal to zero but i don't know how to prove that Ho=Io* sqrt(k/mg)
Here is a doozy
In a magnetic levatation experiment a metallic object is help up in the air suspended under an electromagnet. The vertical displacement of the object can be described by the following nonlinear differential equation.
m(d^2H/dt^2)=mg-k(I^2/H^2)
m=mass of object
g=gravity...