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a) Find solution u of the PDE uyy + 4u = 0 depend on x and y? %3D b) Find the displacement w(x, t) of an elastic string (c 1) subject to the following conditions: (i) The string is initially at rest on the x-axis from x 0 to ∞ ("semi-infinite string"), (ii) For t> 0 the left end of the string (x = 0) is moved in according to 0.5) and 0.02(1 - t) if (0.5

a) Find solution u of the PDE uyy + 4u = 0 depend on x and y? %3D b) Find the displacement w(x, t) of an elastic string (c 1) subject to the following conditions: (i) The string is initially at rest on the x-axis from x 0 to ∞ ("semi-infinite string"), (ii) For t> 0 the left end of the string (x = 0) is moved in according to 0.5) and 0.02(1 - t) if (0.5

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Q6/ a) Find solution u of the PDE uyy + 4u = ở depend on x and y? %3D b) Find the displacement w(x, t) of an elastic string (c 1) subject to the following conditions: (i) The string is initially at rest on the x-axis from x=0 to o ("semi-infinite string"), (ii) For t> 0 the left end of the string (x= 0) is moved in according to 0.5) and 0.02(1- t) if (0.5 <t<1), (iii) Also, lim w(x, t) = 0 for t 2 0. triangular w(0, t) = f(t) = 0.02t if (0 <t< a wave Set up the model with using the Laplace transform and show the details?
Transcribed Image Text:Q6/ a) Find solution u of the PDE uyy + 4u = ở depend on x and y? %3D b) Find the displacement w(x, t) of an elastic string (c 1) subject to the following conditions: (i) The string is initially at rest on the x-axis from x=0 to o ("semi-infinite string"), (ii) For t> 0 the left end of the string (x= 0) is moved in according to 0.5) and 0.02(1- t) if (0.5 <t<1), (iii) Also, lim w(x, t) = 0 for t 2 0. triangular w(0, t) = f(t) = 0.02t if (0 <t< a wave Set up the model with using the Laplace transform and show the details?
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