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From Farhan: | From Farhan: | ||
Any hint on how to go about #16 of 12.3? | Any hint on how to go about #16 of 12.3? | ||
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| + | From [[User:Park296|Eun Young]] : | ||
| + | We already have F(x) and G(t) from #15. | ||
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| + | Using the given conditions, we need to compute coefficients and find <math>\beta</math>. | ||
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| + | We have <math>F(0)=F(L)=F^{''}(0)= F(L)^{''}= 0.</math> | ||
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| + | Using <math>F(0)=F^{''}(0)=0 </math>, we can show that the coefficients of cos and cosh functions are zero. | ||
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| + | Using <math>F(L)=F^{''}(L)=0</math>, we can show that the coefficient of sinh is zero. | ||
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| + | Hence, <math>F(X) = \sin (\beta x)</math>. | ||
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| + | Using <math>F^{''}(L)=0</math>, we can find <math>\beta</math>. | ||
| + | |||
| + | Plug this <math>\beta</math> into G(t) and use the zero initial velocity condition, then we'll get G(t). | ||
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Revision as of 07:04, 19 November 2013
Homework 11 collaboration area
When is this homework due? I don't see any annoucement on the webpage.
From Eun Young:
it's due Wed. 11/20 (See Lesson 36).
From Farhan: Any hint on how to go about #16 of 12.3?
From Eun Young : We already have F(x) and G(t) from #15.
Using the given conditions, we need to compute coefficients and find $ \beta $.
We have $ F(0)=F(L)=F^{''}(0)= F(L)^{''}= 0. $
Using $ F(0)=F^{''}(0)=0 $, we can show that the coefficients of cos and cosh functions are zero.
Using $ F(L)=F^{''}(L)=0 $, we can show that the coefficient of sinh is zero.
Hence, $ F(X) = \sin (\beta x) $.
Using $ F^{''}(L)=0 $, we can find $ \beta $.
Plug this $ \beta $ into G(t) and use the zero initial velocity condition, then we'll get G(t).
From Craig:
For #15 on 12.3, are we supposed to show the work for each of the end conditions, or only part a (simply supported)?
From Eun Young:
#15 is irrelevant to Fig.293.
Question by Ryan Russon: For #8 of p. 556, I am having difficulties finding the solution for this in terms of what should happen with t... I realize that it must meet the IC's and the BC's but I can't figure out a periodic type solution that would vibrate for t>0 Thanks!
