Science:Math Exam Resources/Courses/MATH257/December 2011/Question 02 (b)/Statement

Consider the wave equation

$u_{tt}=u_{xx},\,$

with initial conditions

$u(x,0)=f(x)={\begin{cases}2\sin(2x)&0<x<\pi \\0&{\text{otherwise}}\end{cases}},\;\;u_{t}(x,0)=0.$

(b) Suppose instead the domain is the interval $[0,\pi ]$, with zero (Dirichlet) boundary conditions:

$u(0,t)=0=u(\pi ,t),\,$

and find the solution by separation of variables.