MATLAB: Graphing 2 variables in one equation (can not be transposed)

graphingMATLABplotting

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

Best Answer

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);
Related Question