7/29/2019 Math Model String

1/5

3 440

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2/5

13

23

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3/5

u(x, t) =n=1

2

n22

1

k(1 k)

sin(nk)exp(nt)sin

n

Lx

coscn

Lt

u x t

x t

u(20, 5)

u(x, t) xt

t x

L

k

k = 0.5 k = 0.9 k = 0.1

n n = 1 n = 2n = 3

c

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4/5

n

u(x, t) xt u(x, t)

u(x, t) = 0x t

u(25, 1.25) = 0.75mmu(x, t)

n=1 n = 1 n =

un(x, t) xun(x, t) t

2n22

1

k(1k)

sin(nk)

k

7/29/2019 Math Model String

5/5

sinn

Lx

x = 0 x = L n = 1n = 2

n = 3

coscn

Lt

exp(nt) nn

exp(nt)coscn

Lt

n