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

Laplace transformation: Laplace transform is an integral transform that converts a function of a…

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

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

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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