6. Let 8(t) be the Dirac-delta function. The position u(x, t) of a vibrating string which satisfies Utt – Urr = = 8(t – 1) + 8(t – 2), 0 t, u(0, t) = u(L, t) = 0, t > 0, u(x, 0) = u,(x, 0) = 0, 0

6. Let 8(t) be the Dirac-delta function. The position u(x, t) of a vibrating string which satisfies<br>Utt – Urr =<br>= 8(t – 1) + 8(t – 2),<br>0 < x < L,t > t,<br>u(0, t) = u(L, t) = 0,<br>t > 0,<br>u(x, 0) = u,(x, 0) = 0,<br>0 < x < L.<br>(a) Find the series solution.<br>(b) Does the solution decay in time? Explain the physical interpretation of your result.<br>

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Jun 04, 2022

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6. Let 8(t) be the Dirac-delta function. The position u(x, t) of a vibrating string which satisfies Utt – Urr = = 8(t – 1) + 8(t – 2), 0 t, u(0, t) = u(L, t) = 0, t > 0, u(x, 0) = u,(x, 0) = 0, 0

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