How do I find x for a given value of y?

Question

Dan Teep 2013-11-7

4
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/105189-how-do-i-find-x-for-a-given-value-of-y

评论： Brian Wilkinson 2021-12-17

I'm stuck on this, and no one seems to understand the question. I've defined several variables and made x an array of values. I then made an anonymous function and used fplot to graph it's outputs(F in this case) for every x value. Now, I just need to find the x value that give me F=90. The only way I can think to do it is to solve for x by hand and then type that into matlab but there has to be a simpler way. Any body know how to do this? Here's up to where I'm stuck:

 % Clear all windows and variables 
 clc 
 % Input the values for mass, height, friction coefficient, and gravity 
 m=18; % Mass (kilograms) 
 h=10; % Height (meters) 
 mu=0.55; % Friction coefficient (no units) 
 g=9.81; % Gravitational acceleration (m/s^2) 
 % Input a reasonable range for x 
 x=[-100:100]; 
 % Calculate F given the range of x 
 F=@(x) (mu.*m.*g.*(h.^2 + x.^2).^(1/2))/(x+mu.*h); 
 % Plot F as a function of x 
 fplot(F,[0,100]) 
 title('Force versus Distance') 
 xlabel('Distance (meters)') 
 ylabel('Force (newtons)') 
 grid on 
 % Find the x value that gives F=90 
 ??????????????

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Walter Roberson 2018-11-15

在 MATLAB Online 中打开

(1/2)*(1+erf(p-mi./(sigma*sqrt(2))))

Brian Wilkinson 2021-12-17

在 MATLAB Online 中打开

Here is a code I created that solves for x given y.

% This code solves for x given a value of y. Just set the value for x_low,
% x_high, and y. Enter the formula in terms of x inside the for loop and
% set it equal to y_i. 
x_low=-100; %the lowest value of x that the for loop could possibly output
x_high=100; %the highest value of x that the for loop could possibly output
y=90; %known value of y
x=(x_low+x_high)/2;
for i=1:1000
 m=18; % Mass (kilograms) 
 h=10; % Height (meters) 
 mu=0.55; % Friction coefficient (no units) 
 g=9.81; % Gravitational acceleration (m/s^2) 
 
 y_i=(mu.*m.*g.*(h.^2 + x.^2).^(1/2))/(x+mu.*h);
    
    if y_i<y %the greater than or less than sign may need to be flipped to get a correct value of x after the for loop completes
        x=x-((x_high-x_low)/(2^(i+1))); 
    else
        x=x+((x_high-x_low)/(2^(i+1))); 
    end
end
fprintf('x= %f',x)

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Answer 1

Image Analyst 2013-11-7

7
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/105189-how-do-i-find-x-for-a-given-value-of-y#answer_114425

在 MATLAB Online 中打开

Add this code to the bottom of your code:

Fx = (mu.*m.*g.*(h.^2 + x.^2).^(1/2)) ./ (x+mu.*h);
% Plot the function.
figure;
plot(x, Fx, 'b-');
grid on
% Find the x value that gives F=90.
% This happens when the difference between Fx and 90 is a minimum.
[difference, index_At_F_Equals_90] = min(abs(Fx-90))
% Get the x value at that index.  Print to command window.
x90 = x(index_At_F_Equals_90)

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Walter Roberson 2018-2-6

编辑：Walter Roberson 2018-2-6

abs(Fx-target) will be closer to 0 at the place where the values in Fx are closer to the target value. The location in Fx that is closest to the target will have the smallest absolute difference compared to the target. min() applied to that vector determines the location where the minimum value is. min() with a single output would be just the minimum value itsef; min() with two outputs like is given here also returns the index in the vector at which the minimum was found. So after the min() line, the variable difference will reflect how close you were able to get to the target, and index_At_F_Equals_target will be the location (index) in Fx that was closest. Then you access the vector of x values at that index to determine which x value it was that gave rise to the Fx that was closest to the target. xtarget will not be function after this: it will be the numeric x value at which Fx became closest to the target.

Kalyan Dash 2018-2-6

Thanks Walter. It is much clear now after reading the description. I have used it in my code and it worked.

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Answer 2

Walter Roberson 2013-11-7

4
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/105189-how-do-i-find-x-for-a-given-value-of-y#answer_114424

编辑：Walter Roberson 2013-11-7

在 MATLAB Online 中打开

fzero((x) F(x)-90, [0, 100])

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Dan Teep 2013-11-7

Hmmm, I'm getting an error message at the column with the function name. I guess I'll try using a function file real quick instead of an anonymous one.