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==Homework 8 collaboration area== | ==Homework 8 collaboration area== | ||
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y1 = cos(sqrt(2)t)+ 2/5 cos(t)- 7/5 cos(sqrt(6)t) | 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) | y2 = 1/5 cos(t) + 14/5 cos(sqrt(6)t) | ||
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| + | From [[User:Park296|Eun Young]]: | ||
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| + | If you hit the system of differential equations by the Laplace transform, you'll get | ||
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| + | <math>S^2Y_1 - S = -2 Y_1 + 2Y_2</math> and <math>S^2Y_2 - 3S = 2Y_1 - 5Y_2</math>. | ||
| + | This is a system of two equations. Solve this for <math>Y_1 </math> and <math>Y_2</math> using Cramer's rule or just algebra. | ||
| + | Then, | ||
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| + | <math>Y_1 = \frac{s^3+11s}{s^4+7s^2+6}</math>. | ||
| + | Find <math>y_1</math> using partial fractions. It's similar for <math>y_2</math> | ||
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Revision as of 10:38, 21 October 2013
Homework 8 collaboration area
--- 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)
From Eun Young:
If you hit the system of differential equations by the Laplace transform, you'll get
$ S^2Y_1 - S = -2 Y_1 + 2Y_2 $ and $ S^2Y_2 - 3S = 2Y_1 - 5Y_2 $. This is a system of two equations. Solve this for $ Y_1 $ and $ Y_2 $ using Cramer's rule or just algebra. Then,
$ Y_1 = \frac{s^3+11s}{s^4+7s^2+6} $. Find $ y_1 $ using partial fractions. It's similar for $ y_2 $
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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?
From Andrew:
I don't believe we have to do prob 16 of section 11.1 for the homework, only 11.1.12, 11.1.14, and 11.1.18
From Michael:
Yeah, you're right. Well I guess I got some extra practice in.
