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We have a string with length that is attached at both ends, both at x = 0 and x = 1. The differential equation and boundary conditions that describe the position u as a function of x and are given by Uu(x,t) = c²uzr(x,t), 0 x > 0 %3D %3D where the constant c is the wave speed of the string At time t = 0 we pull the middle of the string to a height h from the equilibrium position so that the position of the string is given by Fx, u(x,0) = #l– x), u:(x,0) = 0 All points on the string have a starting speed of zero at time t = 0, i.e for 0

We have a string with length that is attached at both ends, both at x = 0 and x = 1. The differential equation and boundary conditions that describe the position u as a function of x and are given by Uu(x,t) = c²uzr(x,t), 0 x > 0 %3D %3D where the constant c is the wave speed of the string At time t = 0 we pull the middle of the string to a height h from the equilibrium position so that the position of the string is given by Fx, u(x,0) = #l– x), u:(x,0) = 0 All points on the string have a starting speed of zero at time t = 0, i.e for 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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A = 1 B =1 C= 5 We have a string with length that is attached at both ends, both at x = 0 and x = 1. The differential equation and boundary conditions that describe the position u as a function of x and are given by Uu(x,t) = c²uz(x,t), 0<x < l, u(0,t) = u(1,t) = 0, 0<t<∞, 0 <t<∞ where the constant c is the wave speed of the string At time t = 0 we pull the middle of the string to a height h from the equilibrium position so that the position of the string is given by u(x,0) = 꼭(1-2), 을 <x<l. u;(x,0) = 0 All points on the string have a starting speed of zero at time t = 0, i.e for 0 <x < l. (a) Write down the general solutions for position and speed of this string. Make simplifications as a result of the starting conditions (b) Calculate the coefficients of the general solutions so that you arrive at a solution for position and speed of the string as a function of I and h. To arrive at the solution, the following can be used
Transcribed Image Text:A = 1 B =1 C= 5 We have a string with length that is attached at both ends, both at x = 0 and x = 1. The differential equation and boundary conditions that describe the position u as a function of x and are given by Uu(x,t) = c²uz(x,t), 0<x < l, u(0,t) = u(1,t) = 0, 0<t<∞, 0 <t<∞ where the constant c is the wave speed of the string At time t = 0 we pull the middle of the string to a height h from the equilibrium position so that the position of the string is given by u(x,0) = 꼭(1-2), 을 <x<l. u;(x,0) = 0 All points on the string have a starting speed of zero at time t = 0, i.e for 0 <x < l. (a) Write down the general solutions for position and speed of this string. Make simplifications as a result of the starting conditions (b) Calculate the coefficients of the general solutions so that you arrive at a solution for position and speed of the string as a function of I and h. To arrive at the solution, the following can be used
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