The prоblem оf finding the hоrizontаl displаcement u(x,t) of а finite string of length π with fixed ends, zero initial displacement but an initial velocity ut(x,0)=x, 00. I suggest you use the form above instead of expanding the product! Part (a): Find ALL values of ω that produce nonzero solutions to the PDE and satisfies ALL the homogeneous BC. Also write their corresponding "eigenfunctions''. Part (b): Write a linear superposition of only the functions you wrote in the second answer box to part (a) above. You will use this answer in part (c) next. Part (c): Apply the one nonhomogeneous BC to your answer in part (b) to find the solution u(x,t) to the full BVP. You must use the answer you wrote in part (b) above to get any credit here.
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