graphing 2 variables in one equation (can not be transposed)

Hi i would like to plot c in terms of k in this equation.... X=Y*sqrt((k^2+(c*w)^2)/(((k-m*w^2)^2+(c*w)^2)))

I know all the values except for C and K so really im trying to do a simple 2D x-y plane graph, but cannot do so easily because I can not (or do not know how to) express k in terms of c or vice versa so that i can use the ezplot command or something similar, Ive been racking my brain over this for a few days now, trying different ways, different commands and they all give me some sort of error.

note that... m=2000 ; Y=0.2 ; w=157.08 ; X=0.1 ; ANY HELP WILL BE GREATLY APPRECIATED thank you

Answer 1

[Walter Roberson]

Square both sides to get rid of the sqrt(). Then multiply both sides by the denominator of the right hand side, to get two polynomials equal to each other. Distribute the Y^2 (that used to be Y but you squared) over the (k^2+(c*w)^2) to get Y^2*k^2 + Y^2*c^2*w^2 . Now you have c^2 times coefficients on each side, so subtract the Y^2*c^2*w^2 from both sides so that you end up with all the c^2 on the left and nothing in c on the right. Now you have of the form something1 * c^2 + something2 = something3 and that is clearly a quadratic so proceed to solve it: re-arrange to something1 * c^2 = something3 - something2, then divide through by the something1 to get c^2 = (something3 - something2) / something1 . Square root both sides, remembering to take both negative and positive square roots, and you have c in terms of +/- sqrt(an expression). Remember to plot both roots.

c1 = sqrt(-((X.^2 - Y.^2) .* (m.^2 .* w.^4 .* X.^2 - 2 .* k .* m .* w .^2 .* X.^2 + k.^2 .* X.^2 - k.^2 .* Y.^2))) ./ (w.*(X.^2 - Y.^2));
c = [c1(:),-c1(:)];
plot(k, c);

[Eli Kroitor]

thank you very much for the replies Murali and Walter, I have successfully graphed k against c with your help, I dont know why I thought the equation was untransposable, I guess I just had a brain plug haha :p

Just out of curiosity, can Matlab transpose the equation for you to get one letter in terms of the other for you? cause that would be really helpful to limit any human error

[Walter Roberson]

If you have the Symbolic Toolbox then you can solve() the expression. For example,

syms X Y k c w m
solve( X==Y*sqrt((k^2+(c*w)^2)/(((k-m*w^2)^2+(c*w)^2))), c)

Answer 2

[Murali Krishna]

try this.. create a function

function z = myfun(k,c)
m=2000 ; Y=0.2 ; w=157.08 ; X=0.1;
z = -X+Y*sqrt((k^2+(c*w)^2)/(((k-m*w^2)^2+(c*w)^2)));
end

ezplot(@(k,c)myfun(k,c),[kmin,kmax,cmin,cmax]) in mfile..

[Eli Kroitor]

thank you very much for the replies Murali and Walter, I have successfully graphed k against c with your help, I dont know why I thought the equation was untransposable, I guess I just had a brain plug haha :p

Just out of curiosity, can Matlab transpose the equation for you to get one letter in terms of the other for you? cause that would be really helpful to limit any human error