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"}]
