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Question: please explain it thoroughly...

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1D string and heat conductor Problem 1.1. (4 pts) Consider the 1D vibrating string equation ch.. (t,x) = hn(t,x) + fh(t,z), x E [0, L], f > 0 with the boundary condition h(t,0-0, hz(t, L)=0. Write the most general solution and discuss the qualitative behaviour of the solution (especially its depen- dence on t), can you give a physical interpretation to the f-term? Problem 1.2. (2 pts) Continuing from the above exercise. Now add the initial conditions ㄫㄨ 0, a) = 2 sin3 sin ht (0, z) sin 2L. 2L Now give the complete solution.

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