Suppose a string of length L=1 unit satisfies the following wave equation.u0 < x < 1,t > 0.= 4Suppose the ends of the rope are fixed and the rope is set in motion from the startingposition without initial velocity, i.e.u(0, t) = 0, u(1, t) = 0, t>0,%Du (x, 0) = 0, 0 < x < 1.The position of the rope at the beginning is given by the following function:u(x, 0) = sin(57x)+ 2 sin(77x), 0 < x < 1.Find the solution u (x, t) that expresses the displacement of the rope accordingly.

Given wave equation is, ∂2u∂t2=4∂2u∂x2 This can also be written as, utt=22uxx…

Suppose a string of length L=1 unit satisfies the following wave equation. = 4 0 < x < 1, t > 0. Suppose the ends of the rope are fixed and the rope is set in motion from the starting position without initial velocity, i.e. u(0, t) = 0, u(1, t) = 0, t> 0, U:(x, 0) = 0, 0 < x < 1. The position of the rope at the beginning is given by the following function: u(x, 0) = sin(57x)+2 sin(7Tx), 0 < x < 1. Find the solution u (x, t) that expresses the displacement of the rope accordingly.

Suppose a string of length L=1 unit satisfies the following wave equation. = 4 0 < x < 1, t > 0. Suppose the ends of the rope are fixed and the rope is set in motion from the starting position without initial velocity, i.e. u(0, t) = 0, u(1, t) = 0, t> 0, U:(x, 0) = 0, 0 < x < 1. The position of the rope at the beginning is given by the following function: u(x, 0) = sin(57x)+2 sin(7Tx), 0 < x < 1. Find the solution u (x, t) that expresses the displacement of the rope accordingly.

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Suppose a string of length L=1 unit satisfies the following wave equation.
u
0 < x < 1,
t > 0.
= 4
Suppose the ends of the rope are fixed and the rope is set in motion from the starting
position without initial velocity, i.e.
u(0, t) = 0, u(1, t) = 0, t>0,
%D
u (x, 0) = 0, 0 < x < 1.
The position of the rope at the beginning is given by the following function:
u(x, 0) = sin(57x)+ 2 sin(77x), 0 < x < 1.
Find the solution u (x, t) that expresses the displacement of the rope accordingly.

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