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Homework Statement
Solve the initial boundary value problem
[tex]u_{tt}=c^2u_{xx}[/tex]
[tex]u(-a,t)=0,\quad u(a,t)=0,\quad u(x,0)=\sin(\omega_1 x)-b\sin(\omega_2x) [/tex]
where [itex]a, b, \omega_1, \omega_2[/itex] are positive constants.
Homework Equations
d'Alembert's solution
The Attempt at a Solution
Are these initial/boundary conditions enough to fully solve the problem? All of the textbooks I have seen address only the case where [itex]u(x,0)[/itex] and [itex]u_t(x,0)[/itex] is also given. Or possibly d'Alembert's general solution is not good to use here? Thanks all!