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(Solved): (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 \( u_{u}=c^{2} u_{x x} \), with the

(Extra Credit) A vibrating string with one fixed end and one free end can be described by , with the boundary conditions and . Using separation of variables, find the general solution to the wave equation with these boundary conditions. Now suppose that and are given initial conditions. Find a formula for the unknown coefficients in your general solution.


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o solve the wave equation uu = curr with the boundary conditions u(0,t) = 0 and u(L,t) = 0 using the separation of variables, we assume a
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