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I started this problem by taking the laplace with respect to t. This gave me s*W = x/s^2 - x d/dx * W. I took the derivative of x to be 1. I then solved for W, which gave me W = x/(s^2(s+1)). After this use partial fractions. I am not positive that this is the correct approach - but it matches the answer in the back of the book. Anyone else have any thoughts? | I started this problem by taking the laplace with respect to t. This gave me s*W = x/s^2 - x d/dx * W. I took the derivative of x to be 1. I then solved for W, which gave me W = x/(s^2(s+1)). After this use partial fractions. I am not positive that this is the correct approach - but it matches the answer in the back of the book. Anyone else have any thoughts? | ||
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| + | On prob 16 of 11.1, I set up three piece wise functions to find Bn (odd function An and Ao are 0). | ||
| + | From -pi to -pi/2 I set F(x)=0 | ||
| + | From -pi/2 to pi/2 I set F(x)=x | ||
| + | From pi/2 to pi I set F(x)=0 | ||
| + | |||
| + | From here I solved for Bn. The fourier series I calculated is F(x) = 2/pi sinx - 2/4pi sin2x + 2/9pi sin3x ... | ||
| + | When graphing this, it is similar to the original graph, but seems slightly off. Am I setting up the problem wrong? | ||
[[2013 Fall MA 527 Bell|Back to MA527, Fall 2013]] | [[2013 Fall MA 527 Bell|Back to MA527, Fall 2013]] | ||
[[Category:MA527Fall2013Bell]] [[Category:MA527]] [[Category:Math]] [[Category:Homework]] | [[Category:MA527Fall2013Bell]] [[Category:MA527]] [[Category:Math]] [[Category:Homework]] | ||
Revision as of 14:53, 20 October 2013
Homework 8 collaboration area
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This is the place!
--- From Mnestero:
So after a bunch of algebra to solve the system of equations on prob 12 of 6.7 I got an answer. I often make simple mistakes, so I wanted to see if anyone else got what I have:
y1 = cos(sqrt(2)t)+ 2/5 cos(t)- 7/5 cos(sqrt(6)t) y2 = 1/5 cos(t) + 14/5 cos(sqrt(6)t)
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From Chris:
The example in the book and in our notes doesn't look the same as the problem 5 in 12.12. I'm not even sure how to set up the problem. Can anyone help get me started?
From Mnestero:
I started this problem by taking the laplace with respect to t. This gave me s*W = x/s^2 - x d/dx * W. I took the derivative of x to be 1. I then solved for W, which gave me W = x/(s^2(s+1)). After this use partial fractions. I am not positive that this is the correct approach - but it matches the answer in the back of the book. Anyone else have any thoughts?
On prob 16 of 11.1, I set up three piece wise functions to find Bn (odd function An and Ao are 0). From -pi to -pi/2 I set F(x)=0 From -pi/2 to pi/2 I set F(x)=x From pi/2 to pi I set F(x)=0
From here I solved for Bn. The fourier series I calculated is F(x) = 2/pi sinx - 2/4pi sin2x + 2/9pi sin3x ... When graphing this, it is similar to the original graph, but seems slightly off. Am I setting up the problem wrong?
