Hi Barry,

You're a brave man. Mathematica is quite a bit to take on for the solution to one problem. (But once learned it's a Swiss army knife for math!)

I did not try to look into the physics of the problem, and some of the results look a bit odd. But, here is Mathematica code that solves your equation and provides functions for evaluating the result. It looks bare because I deleted output rather than trying to paste it in in segments. But if you execute it in a notebook it should become clear -- I tired to provide enough comments to make it readable.

Best,

David

(* the equation *)

eq = o^4 - (o - 2 w)^4 == s^4

(* solve the equation symbolically. Mathematica gives a list \

containing 3 solutions.*)

sol = Solve[eq, o]

(* This substitutes real values for s and w and evaluates. Onlty the \

first solution gives a ral number; the other 2 are complex. *)

sol /. s -> 0.419 /. w -> .064

(* This defines a function oo[s,w] as given by the first solution. *)

oo[s_, w_] = o /. sol[[1]]

(* Calling the function with a numbers for s and w returns the \

corresponding value of o. *)

oo[.419, .064]

(* Here is a list of values for s and w, written as a list of lists. *)

values = {

{.419, .064},

{.418, .063},

{.130, .029},

{.098, .024}

};

(* This version of oo takes a list as an argment. *)

oo[{s_, w_}] = o /. sol[[1]]

(* We can map the function onto the list to get a set of resulting \

values for o. *)

oo /@ values

(* We can also make plots. *)

(* Here is a 3D surface over a range of s and w. *)

Plot3D[oo[s, w], {s, .098, .419}, {w, .024, .064},

AxesLabel -> {"S", "W", "O"}]

Plot[oo[0.419, w], {w, .001, .1}, PlotRange -> {0, All},

PlotLabel -> "S = 0.419", AxesLabel -> {"W", "O"}]