For #16, I am just not sure how u can eliminate the 3 constants in front of cos, cosh, and sinh to be zero... Just to be sure, we equate F(0) and F(0) and equate F(L) and F(L) correct? With this I get that A+C = -(beta^2)*(A+C). How can we assume both A and C are zero? For the second equation, I am not at all sure how the sinh coefficient goes to zero...I am getting A = -A*beta^2, B = -B*beta^2, and so forth...suggestions?
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:
You do not need boundary conditions for #15. See Lesson 38 to get some hints.
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!
