Plot a Potential Energy Graph

I have the function U(x) = a x^2 - b x^3 for potential energy and want to plot it with all of a and b positive values. how do i plot this function?

[darova]

Did you try plot? Can you attach your code?

[Allen Ruff]

syms a b x

U(x)= a*x^2+b*x^2

fplot(@(x) U(x))

This gave me a graph with a warning

[Pooja Lalan]

fplot is used to plot a function of one variable. For instance, if U is a function of only x i.e. U(x), a and b must be constants.

a = 1;

b = 1;

U = @(x) a.*x.^2 - b.*x.^3;

fplot(U)

In the live editor, you can use slider controls to vary a and b to get different line graphs.

However, if you want to plot U as a function of a and b, you can fix x and use fsurf instead.

It is not quite clear how "with all of a and b positive values" translates to a graphic in this context. Is it an animation or some kind of a 3-D visual? Can you point to an example of something similar?

[DGM]

"all of a and b positive values"

You do realize that's an infinite domain, right? You're going to have to settle for less than infinite.

Answer 1

[Erik Huuki]

First solve for the roots of the equation. As long as a and b are positive there will be an answer

Turns out for this case it will always bounce off the origin and intersect at a positive value so long as a and b are positive

a = randi([1,10]);
b = randi([1,10]);

r = roots([-b,a]);
x = linspace(0,r);
y = a.*x.^2-b.*x.^3;
plot(x,y)