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A uniform string stretched between the points (0,0) and (L, O) is given an initial displacement: y = f(x) = x for 0 SXSL and released from rest. Find the subsequent displacement y(x, t). Governing PDE: Ә2y = 16 д?у [0 < x <L,t> 0] ot? дх? Obtain the expression for the coefficient by integrating the resulting Fourier series and include it in the final answer.

apy მე-2 A uniform string stretched between the points (0, 0) and (L, O) is given an initial displacement: y = f(x) = x, 0<x<L and released from rest. ay 16- Its Partial differential equation is ət2 Initial Condition: Initial Displacement: y(x,0) = f(x) = x, OSXSL, yx (3,0) = 0, 0<x<L Boundary Conditions: ( As rod is released from rest) y(0, 1) = y(L, t) = 0, t > 0