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Here u(x,t) refers to D'ALembert's solution for the one dimensional wave. L represnets the legnth of the string and c, the speed of the wave.

Find u(3/4,2) where l=c=1 f(x) = x(1-x), g(x) = x^2 (1-x)

Ok i know that from earlier that i ahve to extend g as an even periodic function over this interval

But what about f? Does f have to be extended ?

For teh extension of g... Do i simply move that function to right?

so [tex] g_{1} (r) = r^2 (1-r) [/tex]

for [tex] g_{2} (r) = (-r-\frac{1}{2})^2)[1-(-r-\frac{1}{2})] [/tex] over the interval [5/4,7/4]

and finally [tex] g_{3} (r) = (r-1)^2)[1-(r-1)] [/tex] over the interval [7/4,2]

am i going in the right direction??

Simialr question i have is

If [itex] f(x) = x^2 (1-x)^2, g(x) = 1, \partial u/ \partial x (0,t)=0, c=1, find u(3/4,7/2)[/itex]

does f(x) have to be extended

if so would it be extended by a polynomial of degree 4? in which case

for [1,2] (x-1.5)^4

for [2,3.5] (2.5-x)^4 [/tex]

your help would be greatly appreciated!

p.s. the other question was not required to be answered tahts why you don't see that one, thanks!

Find u(3/4,2) where l=c=1 f(x) = x(1-x), g(x) = x^2 (1-x)

Ok i know that from earlier that i ahve to extend g as an even periodic function over this interval

But what about f? Does f have to be extended ?

For teh extension of g... Do i simply move that function to right?

so [tex] g_{1} (r) = r^2 (1-r) [/tex]

for [tex] g_{2} (r) = (-r-\frac{1}{2})^2)[1-(-r-\frac{1}{2})] [/tex] over the interval [5/4,7/4]

and finally [tex] g_{3} (r) = (r-1)^2)[1-(r-1)] [/tex] over the interval [7/4,2]

am i going in the right direction??

Simialr question i have is

If [itex] f(x) = x^2 (1-x)^2, g(x) = 1, \partial u/ \partial x (0,t)=0, c=1, find u(3/4,7/2)[/itex]

does f(x) have to be extended

if so would it be extended by a polynomial of degree 4? in which case

for [1,2] (x-1.5)^4

for [2,3.5] (2.5-x)^4 [/tex]

your help would be greatly appreciated!

p.s. the other question was not required to be answered tahts why you don't see that one, thanks!

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