Consider a semi-infinite elastic string that extends along the x-axis from x = 0 to infinity and let u(x, t) be its deflection about the equilibrium position. Suppose that the endpoint at x = 0 is free to move vertically, so that axu (0, t) = 0. At some time, denoted as t = 0, the string is suddenly hit such that the initial deflection and velocity can be idealised as u(x,0) = 0, du(x,0) = g(x) = 508(x - 20), respectively. Determine u(x, t) for t> 0 using a suitable type of Fourier transformation. Leave your final answer in terms of the signum function (see below).
Consider a semi-infinite elastic string that extends along the x-axis from x = 0 to infinity and let u(x, t) be its deflection about the equilibrium position. Suppose that the endpoint at x = 0 is free to move vertically, so that axu (0, t) = 0. At some time, denoted as t = 0, the string is suddenly hit such that the initial deflection and velocity can be idealised as u(x,0) = 0, du(x,0) = g(x) = 508(x - 20), respectively. Determine u(x, t) for t> 0 using a suitable type of Fourier transformation. Leave your final answer in terms of the signum function (see below).
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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