Using support, a long taut string is fixed along the positive x-axis. At time t = 0, the support is removed and gravity is permitted to act on the string. Assuming that the end x = 0 is fixed, the initial, boundary-value problem describing displacements y(x, t) of points in the string is:∂^2?/∂?^2 = ?^2*∂^2?/∂?^2 − ?, ? > 0, ? > 0?(0, ?) = 0, ? > 0 ?(?, 0) = 0, ? > 0??(?,0)/dt = 0,? > 0 Where g is gravity and is equal to 9.81. Use Laplace transforms to solve this problem.Q1. What is the value of y(x,t) at x=c and t=0.5? Submit your answer to one decimal place. Using support, a long taut string is fixed along the positive x-axis. At time t=0, the supportis removed and gravity is permitted to act on the string. Assuming that the end x = 0 is fixed,the initial, boundary-value problem describing displacements y(x, t) of points in the stringis:2²yat²a² yəx²y (0,t) = 0,t> 0y(x,0) = 0, x>0-g,x>0,t> 0dydtWhere g is gravity and is equal to 9.81. Use Laplace transforms to solve this problem.Q1. What is the value of y(x,t) at x-c and t-0.5? Submit your answer to one decimal place.-(x,0) = 0, x > 0

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Answered: Using support, a long taut string is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Using support, a long taut string is fixed along the positive x-axis. At time t = 0, the support is removed and gravity is permitted to act on the string. Assuming that the end x = 0 is fixed, the initial, boundary-value problem describing displacements y(x, t) of points in the string is:

∂^2?/∂?^2 = ?^2*∂^2?/∂?^2 − ?, ? > 0, ? > 0

?(0, ?) = 0, ? > 0 ?(?, 0) = 0, ? > 0

??(?,0)/dt = 0,? > 0

Where g is gravity and is equal to 9.81. Use Laplace transforms to solve this problem.
Q1. What is the value of y(x,t) at x=c and t=0.5? Submit your answer to one decimal place.