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 · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos

Mar 06, 2019

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Page 1:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 2:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos

𝜕2p

𝜕x2−

1

c2

𝜕2p

𝜕t2= 0

B𝜕4uy

𝜕x4+ m

𝜕2uy

𝜕t2= 0

𝜕2uy

𝜕x2−

ρ

𝐺

𝜕2uy

𝜕t2= 0

𝜕2ux

𝜕x2−

ρ

E′

𝜕2ux

𝜕t2= 0

Page 3:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos

y− x, t = y cos(ωt − kx)

y+ x, t = y cos(ωt + kx)y x, t = y− x, t + y+ x, t = 2 y sin(kx)cos ωt

ω

y1 x, t = y cos(ωt − kx)

y2 x, t = y cos(ωt − kx + θ)y x, t = y1 x, t + y2 x, t = 2 ycos

θ

2sin(ωt − kx + θ)

Ф

Page 4:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 6:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos

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Page 7:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 8:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 9:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 10:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos

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Page 11:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos

Page 12:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 13:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos

Page 14:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 15:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 16:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 17:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 18:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 19:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 20:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos

Page 21:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 22:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 23:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos

Page 24:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 25:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 26:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos

Page 27:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos

Page 28:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos
Page 29:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos

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Page 30:  · y−x,t=ycos(ωt−kx) y+x,t=ycos(ωt+kx) yx,t=y−x,t+y+x,t=2ysin(kx)cosωt ω y1x,t=ycos(ωt−kx) y2x,t=ycos(ωt−kx+θ) yx,t=y1x,t+y2x,t=2ycos