3) Both ends of a string are attached to two walls at a height of 0 cm. The string is 25 cm long and the walls are separated by 25 cm. The horizontal distance between the walls is measured by the variable x, 0≤x≤ 25. Initially, t=0, the string is stretched to have its height, u(x), given by u(x) = 4sin(2лx/25). Initially the string is at rest, that is it has no vertical velocity at any point. The speed of a wave propagating along the string is 3cm/sec. A) Write the wave equation for the string. B) Write the boundary conditions for the string (x = 0 and x =25). C) Solve for the height, u(x, t), of the wave for t > 0.
3) Both ends of a string are attached to two walls at a height of 0 cm. The string is 25 cm long and the walls are separated by 25 cm. The horizontal distance between the walls is measured by the variable x, 0≤x≤ 25. Initially, t=0, the string is stretched to have its height, u(x), given by u(x) = 4sin(2лx/25). Initially the string is at rest, that is it has no vertical velocity at any point. The speed of a wave propagating along the string is 3cm/sec. A) Write the wave equation for the string. B) Write the boundary conditions for the string (x = 0 and x =25). C) Solve for the height, u(x, t), of the wave for t > 0.
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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Transcribed Image Text:3) Both ends of a string are attached to two walls at a height of 0 cm. The string is 25 cm
long and the walls are separated by 25 cm. The horizontal distance between the walls is
measured by the variable x, 0≤x≤ 25. Initially, t=0, the string is stretched to have its
height, u(x), given by u(x) = 4sin(2x/25). Initially the string is at rest, that is it has no
vertical velocity at any point. The speed of a wave propagating along the string is
3cm/sec.
A) Write the wave equation for the string.
B) Write the boundary conditions for the string (x = 0 and x =25).
C) Solve for the height, u(x, t), of the wave for t > 0.
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VIEWStep 2: Writing the wave equation with initial and boundary conditions
VIEWStep 3: Finding the spacial solution of u(x,t)
VIEWStep 4: Finding the temporal solution of u(x,t)
VIEWStep 5: Determining the solution using the Superposition principle and Fourier series
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