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(Extra Credit) A vibrating string with one fixed end and one free end can be described by uu=c2 ...
(Extra Credit) A vibrating string with one fixed end and one free end can be described by uu?=c2uxx?, with the boundary conditions u(0,t)=0 and ux?(L,t)=0. Using separation of variables, find the general solution to the wave equation with these boundary conditions. Now suppose that u(x,0)=f(x) and ul?(x,0)=g(x) are given initial conditions. Find a formula for the unknown coefficients in your general solution.