(i) Suppose that an infinite string has an initial displacement x+1, -1x0 1-2x, 0 x...

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(i) Suppose that an "infinite string" has an initial displacement x+1, -1≤x≤0 1-2x, 0 ≤ x ≤ 1/2 0, I < -1 and x > 1/2 and zero initial velocity u, (,0) = 0. Write down the solution of the wave equation u(a,0) = f(x) = = UttUxx with ICs u (x, 0) = f (x) and u₂(x, 0) = 0 using D'Alembert's formula. Illustrate the nature of the solution by sketching the ur-profiles y = u(x, t) of the string displacement for t = 0, 1/2, 1,3/2. W (i) Suppose that an "infinite string" has an initial displacement x+1, -1≤x≤0 1-2x, 0 ≤ x ≤ 1/2 0, I < -1 and x > 1/2 and zero initial velocity u, (,0) = 0. Write down the solution of the wave equation u(a,0) = f(x) = = UttUxx with ICs u (x, 0) = f (x) and u₂(x, 0) = 0 using D'Alembert's formula. Illustrate the nature of the solution by sketching the ur-profiles y = u(x, t) of the string displacement for t = 0, 1/2, 1,3/2. W

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