Writing a Function for Plotting

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.

Answer 1

[Paulo Silva]

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.

[Big Meech]

Will do. Is it possible you can check over what I have when I'm done?

[Paulo Silva]

Tip: in the first part you just need to replace the x on the condition by some equivalent expression based on two other variables

I will try to check your code if I can or someone else might do it, the second part is very easy, good luck

[Matt Fig]

+1.

I would add to what Paulo said. An IF statement does not pick out elements of an array. So if you plan on passing in a vector of values for W, use logical indexing instead of an IF statement. Read this, there are a couple of examples of logical indexing....

docsearch('matrix indexing')

[Paulo Silva]

Good advice Matt and congratulations for your new MATLAB Answers Editor status :)

[Matt Fig]

Thanks Paulo!

Answer 2

[Big Meech]

This is what I have now. I think it is right. I use the elseif because if I just use else it returns ans= 1 then x=0.1250

function spring(W,k1,k2,d)

if ((W/k1)<d)
    x= W/k1

elseif ((W + 2*d*k2)/(k1 + 2*k2) >=d)
    x=(W + 2*d*k2)/(k1 + 2*k2)

end

Also is it possible to write another function that uses the function I just wrote to graph it all within the same .m file?

[Big Meech]

would I have to create a fplot something like this?

fplot(spring,[0,3000])

[Paulo Silva]

Like I said before you don't need that elseif condition, just put else there, also your function must return something, in that case it should return the x value, and finally you should put the ; after the x value assignment (no x value will appear on the command window)

function x=spring(W,k1,k2,d)

if ((W/k1)<d)

x= W/k1;

else

x=(W + 2*d*k2)/(k1 + 2*k2);

end