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(1 point) The displacement u(x, t) of a semi-infinite thin 1D elastic string is given by: au at2 a2 au da2x > 0,t> 0 u(0,t) = { sin(at), 05433 lim u(x,t) = 0, t > 0 1 t> 2 > u(x,0) = 0, ut(x,0) = 0, x > 0 Use the Laplace transform to solve for u(x, t). Put your answer in the following form, i.e., find u1(2, t) and u2(x, t) such that u1(x, t), tad u(x, t) = u2(x, t), St + 3 uz(x, t), t>" + 3 Also, simplify your answers. u1(x, t) uz(x, t) u3(2,t) = =