MATLAB: Writing a Function for Plotting

MATLAB

Hello, Here is a link to my assignment.
http://viewer.zoho.com/docs/wyaXc
I need help with the second part. The first part was simple. Here is what I have.
function spring(W,k1,k2,d)
if (x<d)
    x= W/k1
else (x >=d)
    x=(W+ (2 .* (k2) .* d)/((k1) + (2.*(k2)))) 
end
How would I plot this? See link as reference.
Thanks for help in advance.

Best Answer

Your first part is wrong, please tell me how can you compare x with d without having x defined first?
Please test your functions first so we can help you better, the statement
else (x >=d)
is also wrong, it should be something similar to
elseif (x >=d)
but that condition is irrelevant, it should only be
else
because it's the opposite condition from the if, it takes all the values that the if doesn't "catch".
Your second expression should be
x=(W + 2*d*k2)/(k1 + 2*k2)
I made the plotting but I won't post the code because you must do your own homework and learn with your own mistakes.
Edit: ok here' the code, I'm just posting it because Big Meech shown that he's working on the homework and the use of logical indexing is the way to go (Matt Fig sugestion), the following code works just fine but it's slower than the one using logical indexing.
function x=spring(W,k1,k2,d)
if ((W/k1)<d)
    x= W/k1;
else
    x=(W + 2*d*k2)/(k1 + 2*k2);
end
Script for the plot, this is not one optimized version, there's no pre-allocation of the x and the plot is called too many times (each time creating a new object thus wasting time and memory)
clf
hold on
st=5; %step


for W=0+st:st:3000-st;
x=spring(W,k1,k2,d);
plot(W,x)
end
extra text and lines
line([0 k1*d],[d d],'linestyle','--','color',[1 0 0])
line([k1*d k1*d],[0 d],'linestyle','--','color',[1 0 0])
text(0,d,'d')
text(k1*d,0,'k_1*d')
text(k1*d/2,d/2,'x=W/k_1')
text(k1*d+k1*d/6,d+d/6,'x=(W + 2*d*k_2)/(k_1 + 2*k_2)')
Just for fun I tested both ways to do it, logical indexing got also the pre-allocation of x memory space.
%constant values used in the test
k1 = 10000; % N/m;



k2 = 15000; % N/m;
d = 0.1;
W = 500; %N
st=0.1; %step
Time required for the plot to be done with logical indexing: 0.029902 seconds.
Time required for the plot to be done with if and else: 23.764888 seconds.
It's a big difference!
Last Edit
Here's the version with logic indexing
    function x=spring2(W,k1,k2,d)
    %This time the function is called spring2 not just spring
    %W is now a vector, not just a number
    x=0*W; %create the local x vector with the size of W and full of zeros
    x((W/k1)<d)= W(W<k1*d)/k1;
    x((W/k1)>=d)=(W(W>=k1*d) + 2*d*k2)/(k1 + 2*k2);
    end
Script that calls the function (don't put it in the same file as the function!!!)
%initial values
k1 = 10000; % N/m;
k2 = 15000; % N/m;
d = 0.1;
st=0.1; %step
x=zeros(1,3000/st-2); %pre-allocate memory for the x vector
W=0+st:st:3000-st; %create the W vector
x(1:numel(W))=spring2(W,k1,k2,d); %call the function just once
plot(W,x) %plot the results just once (only creates a plot object)
If you want to compare the time it takes to execute use the tic and toc functions, the version with pre-allocating of memory and logic indexing is the best way to do it.
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