Want to plot theoretical curve

I want to plot this two equation . actually these are two theoretical model. I do not have any data for i and t. I know the form of the curve and attaching the plot. I was trying by using some value for t , but getting half bell shaped curve.

equations are i^2/(〖i2〗_max^ )=1.2254(t_mAX/t){〖1-exp[-2.3367( t^2/(t_max^2 ))]}〗^2 i^2/(i_max^2 )=1.9542(t_mAX/t){〖1-exp[-1.2564( t/(t_max ))]}〗^2

Matlab code

x=(1:20);

A=(x./max(x));

C=(A).^2;

for i=1:20

D(i)=[1.2254*(1./A(i))*[1-exp(-2.3367.*C(i))]^2];

end

plot (C,D)

[Image Analyst]

I have two questions

1. Do you have a question ? Or are you merely telling us what you're going to do?
2. If you want us to fix your code, can you attach your code with the paper clip icon?

[Star Strider]

Create a vector for t/t_max as:

ttm = linspace(0,5);

then take it or its inverse (use (1./ttm) for the inverse, and (ttm.^2) or ((1./ttm).^2) — note the ‘.’ — for the squared terms) and use that in your equation. If you simply want to plot the curve, it’s not necessary to know what t or t_max actually are.

[sudipta]

@ Star Strider, I want to plot the curve only. I have attached the code. I have tried giving value for X but tat selection are not proper for the type of plot I want to get. But how can I plot without giving some input range for X? Thanks

Answer 1

[Roger Stafford]

The scale factors 1.2254 and 2.3367 in your first theoretical equation have been so chosen that the function

   f(z) = 1.2254/z*(1-exp(-2.3367*z^2))^2

attains a maximum value of 1 just at z = 1. Since z here is simply a ratio t/t_max where t_max indicates the value of t where f(t/t_max) attains its maximum value, there is no way you can plot the value of f(t/t_max) against just the variable t without further information. Similarly there is no way you can plot just i without some further information about i_max. If you know both t_max and i_max, you could then find the i against t curve with:

 i = i_max*sqrt(f(t/t_max))

A similar statement holds for the second theoretical equation.

In other words you cannot plot the curve of i against t just from the plot you have exhibited above without also knowing both i_max and the corresponding t_max.

(Note: Calling it t_max is somewhat misleading because it refers to a value of t where i is maximum.)