Answered: Q2) Find a formal solution to the…

Q2) Find a formal solution to the vibrating string problem governed by the given initial-boundary value problem. 00, u(0,t) = u(1,t) = 0, t>0, %3D u(x,0) = 2x(1 - x), 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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Concept explainers

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

Q2) Find a formal solution to the vibrating string problem governed by the
given initial-boundary value problem.
0<x<1,
t>0,
%3D
u(0,t) = u(1,t) = 0,
t>0,
u(x,0) = 2x(1 - x),
0<x<1,
du
a (x,0)
= sin 7Tx,
0 <x<1
ητα
Referring to the general formal solution for the vibrating string problem, u(x,t) = 2 ]an cost+b, sin
sin
provide the values for a, L, and the coefficients a, and b,.
Start
n=1
by giving the value for a.
(Type an exact answer, using x as needed.)

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