Plots for second order control system in the same graph

I'm been trying to graph this equation without success.I keep getting an error message that says:Warning: Imaginary parts of complex X and/or Y arguments ignored.

Note: input is in radiant.

Here is my code:

% Exersice 11

x = input('Please enter vector x in degree: ');

z = [0.1 0.2 0.4 0.7 0.9];

y1 = 1-1/sqrt(1-z(1,1).^2).*exp(-z(1,1).*x).*sin(sqrt(1-z(1,1).^2)).*x+acos(x);

y2 = 1-1/sqrt(1-z(1,2).^2).*exp(-z(1,2).*x).*sin(sqrt(1-z(1,2).^2)).*x+acos(x);

y3 = 1-1/sqrt(1-z(1,3).^2).*exp(-z(1,3).*x).*sin(sqrt(1-z(1,3).^2)).*x+acos(x);

y4 = 1-1/sqrt(1-z(1,4).^2).*exp(-z(1,4).*x).*sin(sqrt(1-z(1,4).^2)).*x+acos(x);

y5 = 1-1/sqrt(1-z(1,5).^2).*exp(-z(1,5).*x).*sin(sqrt(1-z(1,5).^2)).*x+acos(x);

plot(x,y1,x,y2,x,y3,x,y4,x,y5, 'm'), xlabel('x in radiands'), ylabel('y(x)') ,title('1-1/{\surd}(1-\zeta^2)e^-^\zeta^xsin{\surd}(1-\zeta^2)x+cos^-^1(x)'), grid, legend('\zeta = 0.1','\zeta = 0.2','\zeta = 0.4','\zeta = 0.7','\zeta = 0.9')

[Azzi Abdelmalek]

What is the problem?

[Carlos]

I should get a sinusoidal graph for each zeta plugged in and what I'm getting is a strange line.

See attached screenshots

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Answer 1

[Paul]

Two things are wrong. One is the parenthesis before .x which should be on the end. The second is the acos(x) which should be acos(z(...)). Also it doesnt make sense that you ask x in degrees while it should be radians:

x = input('Please enter vector x in radians: ');
z = [0.1 0.2 0.4 0.7 0.9];
y1 = 1-(1/sqrt(1-z(1,1).^2)).*exp(-z(1,1).*x).*sin(sqrt(1-z(1,1).^2).*x+acos(z(1,1)));
y2 = 1-1/sqrt(1-z(1,2).^2).*exp(-z(1,2).*x).*sin(sqrt(1-z(1,2).^2).*x+acos(z(1,2)));
y3 = 1-1/sqrt(1-z(1,3).^2).*exp(-z(1,3).*x).*sin(sqrt(1-z(1,3).^2).*x+acos(z(1,3)));
y4 = 1-1/sqrt(1-z(1,4).^2).*exp(-z(1,4).*x).*sin(sqrt(1-z(1,4).^2).*x+acos(z(1,4)));
y5 = 1-1/sqrt(1-z(1,5).^2).*exp(-z(1,5).*x).*sin(sqrt(1-z(1,5).^2).*x+acos(z(1,5)));
figure;
plot(x,y1,x,y2,x,y3,x,y4,x,y5, 'm'), xlabel('x in radiands'), ylabel('y(x)') ,title('1-1/{\surd}(1-\zeta^2)e^-^\zeta^xsin{\surd}(1-\zeta^2)x+cos^-^1(x)'), grid, legend('\zeta = 0.1','\zeta = 0.2','\zeta = 0.4','\zeta = 0.7','\zeta = 0.9')

It would also be easier to just use z(2) instead of z(1,2) etc. and using a for loop like Mischa suggested would save you the copy paste code.

Answer 2

[Mischa Kim]

Carlos, check out

 function myDE()

 prompt   = {'xmin:','xmax:'};
 name     = 'Input x-range';
 numlines = 1;
 xlimits  = inputdlg(prompt,name,numlines);

 N = 100;
 x = linspace(str2num(xlimits{1}),str2num(xlimits{2}),N);
 z = [0.1 0.2 0.4 0.7 0.9];

 hold all
 for ii = 1:numel(z)
    y = 1 - (1/sqrt(1-z(ii)^2))*exp(-z(ii)*x).*sin(sqrt(1-z(ii)^2)*x...
          + acos(z(ii)));
    plot(x,y)
 end
 end

[Carlos]

This is beyond my course scope. Could you simplify using more or less what I have above?

Thanks.