I don't think I've ever came across a question like this before in my life. I'm a chemistry major so I may never see Fourier coefficient types questions ever again and I've been having trouble finding help in the internet and the course doesn't even come with a book. Anyone willing to help with this problem please?

 

http://en.wikipedia.org/wiki/Fourier_series

Scroll down to definition. a_n and b_n are the coefficients.

Just plug your eqns into the formula and you should be good to go.

 

I pressed on a littler further and found that a 1Hz sine wave should have a time of 1 second.

For ωo I used the formula f=1/T thus making my ωo=2*pi*(1/1)=> 2pi

Now I'm not sure what my y(t) function should be. I took a guess based on the problem:

y(t) = Sin(t) + 0.1(Sin(t))^2 + 0.01(Sin(t))^3

 

To find the constants using my questionable y(t) as my function I started plugging that equation in to find the coefficients:

ao=1/T*Integral(0 to T) [y(t)] dt
ao=1*Integral(0 to 1second) [Sin(t) + 0.1(Sin(t))^2 + 0.01(Sin(t))^3] dt => 0.5

an=2/T*Integral(0 to T) [y(t) * Cos (n*ωo*t] dt

a1=2*Integral(0 to 1second) [Sin(t) + 0.1(Sin(t))^2 + 0.01(Sin(t))^3 * Cos(1*2pi*t)] dt => -0.02

Can Any Help Out? I still don't think I have this right.

 

Looks pretty good to me. It will probably be easier to compute the coefficients for a general a_n and b_n and then once you have that formula, you can just plug in 1, 2, 3... for whatever coeffs you need.

Also, unless you're allowed to use maple or something for solving integrals, it **may** be easier to use the complex FS... usually integrating exponentials is easier than things like sin^3*cos.

Even so... have fun integrating that function haha.

Your approach looks pretty good to me though.

Except:

a1=2*Integral(0 to 1second) [Sin(t) + 0.1(Sin(t))^2 + 0.01(Sin(t))^3 * Cos(1*2pi*)] dt => -0.02

Check your distribution of the cos factor in this line.

 

I took your advice and plugged the 1 through 5 coefficients into mathmatica but it looks like none of the n's come out to zero, they are all around -0.01 which seems a bit odd since I originally figured some of them would be odd functions and equate to zero, thus giving me a basis for the last sentence in the problem.

 

I originally figured some of them would be odd functions and equate to zero, thus giving me a basis for the last sentence in the problem.

When applying symmetry to these equations, you want to use the the function as a whole... that is, you want to check the symmetry of y(t) to determine if the a_n's or b_n's would be zero... not the individual components. If the function (y(t)) is Odd, then all the a_n's are zero and if Even, B_n's are zero.

It is pretty weird that you get pretty similar answers for each coefficient... usually the coefficients decrease as n increases. I don't have time right now, but if no one has helped out anymore by tomorrow, i'll try and crunch some numbers and see if i can come up with something.

I'm not completely sure what the conclusions should be... but i'm gonna guess that they are going to come out to be mostly odd harmonics.

I say that because of a quote i read:

"The odd harmonics are significant, because the even harmonics tend to cancel each other out"

In reference to total harmonic distortion (THD).

Good luck! Hopefully someone will help you out a little more soon!