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Consider an elastic string of length L whose ends are held fixed. The string is set...

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Question

Physics

Consider an elastic string of length L whose ends areheld fixed. The string is set in motion with no initial velocityfrom an initial position

u(x, 0) =f(x).

Let

L = 10

and

a = 1

in parts (b) and (c). (A computer algebra system isrecommended.)

f(x) =

16x
L
,		    0≤x≤
L
4
,
4,    
L
4
<x<
3L
4
,
16(L −x)
L
,		    
3L
4
≤x≤L

(a) Find the displacement

u(x,t)

for the given initial position

f(x).

(Use a to represent an arbitrary constant.)
u(x, t) =

∞
n = 1

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