Solving and plotting spring constant vs Force

I'm working on a simple spring question which requires me to plot the spring constant vs the force. I am given a number of constants and need to plot the Force for a given range for the k constant.

I am trying to obtain a value for "F" over a k range of 100000 to 800000. I can't seem to be able to obtain and store values of F in order to plot them against the k values.

here is my code:

   %Declare constants and range along axis
  c = 50*10^3;
  x = 2.5*10^-2;
  k = [100:1:800]*10^3;

for i = 1:length(k)
    y = (F/k)+sqrt(F/c);
    F(i) = solve(y == x, F);
   end

%Plots the graph
plot(k, F)
xlabel('k');
ylabel('Force (N/m)');
title('Force vs. k');

What am I doing wrong?!

Thanks

Answer 1

[Roger Stafford]

There is no need to use the symbolic function 'solve' at each of 701 steps. If properly used, 'solve' could give you a general formula, which you could then use to numerically compute the F that corresponds to each k.

Actually you don't even need 'solve' at all for this simple equation. It can easily be converted to a quadratic equation which you can use to solve for F as a function of k. My solution for that is:

 F = x^2*k*c./(x*c+k/2+sqrt(x*k*c+k.^2/4));

(Note: The usual form of the quadratic equation solution would require a subtraction of two large and nearly equal quantities which reduces computation accuracy. Accordingly I have "rationalized" it to place the square root part in the denominator where these quantities are summed rather than subtracted, and that improves its accuracy.)

If obtaining a plot is the only requirement in your problem, you could just as well find k as a function of F which is even easier to do. It should be fairly easy to determine the interval of F values which will place k between the limits you have set for it. You could still do the plot as "plot(k,F)" even if it is now F that will be stepped off in equal increments.