# Why is my graph not right?

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chris henkel on 18 Dec 2017
Commented: Star Strider on 19 Dec 2017
Im trying to make this graph. I was unable to find symbols so I just used numbers for most of the equation (the first one). I need to plot (delta w). Ive added an attachment with the equation and what the graph should look like, if someone could help. This is what I have tried but I keep getting the wrong curve:
>> w0 = 10.^14
w0 =
1.0000e+14
>> y = 5*10.^12
y =
5.0000e+12
>> e3 = 12.1
e3 =
12.1000
>> e4 = 10
e4 =
10
>> w = 50*10.^12:10.^12:150*10.^12;
>> e1 = ((e4)-((e3)-(e4)))*(((2*(w0))*(w))/(((4*((w).^2))+((y).^2))));
>> plot(w,e1)

Star Strider on 19 Dec 2017
Since this was due three weeks ago, I decided to code it myself for fun. There actually seem to be some errors in the homework assignment either in the constants or the range of the independent variable. It may also be that there should be an offset, perhaps something like ‘(dw - w0)’ or some such that would centre the independent variable appropriately to reproduce the plots as posted. (I just experimented with the independent variable until I got the plots to work.)
This produces the plots:
dw = linspace(-25, 25) * 1E+12;
w0 = 1E+14;
gma = 5E+12;
est = 12.1;
einf = 10;
e1 = @(dw) einf - (est - einf)*2*w0*dw./(4*dw.^2 + gma.^2);
e2 = @(dw) (est - einf) * gma*w0./(4*dw.^2 + gma.^2);
n = @(dw) sqrt(e1(dw) + sqrt(e1(dw).^2 + e2(dw).^2))/sqrt(2);
kpa = @(dw) sqrt(-e1(dw) + sqrt(e1(dw).^2 + e2(dw).^2))/sqrt(2);
figure(1)
subplot(2,2,1)
plot(dw, e1(dw))
ylabel('\epsilon_1')
grid
subplot(2,2,3)
plot(dw, e2(dw))
ylabel('\epsilon_2')
xlabel('\omega')
grid
subplot(2,2,2)
plot(dw, n(dw))
ylabel('\it{n}')
grid
subplot(2,2,4)
plot(dw, kpa(dw))
ylabel('\kappa')
xlabel('\omega')
grid
Experiment to get the result you want.