4. (a) A finite string of length has the left end fixed and the right end free. The ㅠ initial displacement is zero, and the initial velocity is given by the function (x) = sin (). Find the vibrations of the string for t > 0, 0≤x≤n; that is, solve =a²uzz TER Uμ = u (t,0)=u, (t, x) = 0 (2) u (0, x) = 0, u, (0, 2) = sin( (b) Now assume that the string is infinite with the same initial conditions. Solve the problem using d'Alembert's formula.

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