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The longitudinal displacement of a vibrating elastic bar shown in the figure satisfies the wave equation a = d'u d'u ax² di² 00 and the conditions: ..... ди = 0, t>0 ax du = 0, 0 < x

The longitudinal displacement of a vibrating elastic bar shown in the figure satisfies the wave equation a = d'u d'u ax² di² 00 and the conditions: ..... ди = 0, t>0 ax du = 0, 0 < x

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Solve the wave equation, subject to the conditions cited in the problem.

The longitudinal displacement of a vibrating elastic bar shown in the figure satisfies the wave a'u d'u equation a 0<x< L, t> 0 and the conditions: du du = 0, ax x L = 0, t> 0 ax x = 0 du u(x, 0) = x, = 0, 0 < x < L. t= 0 Hu(x, 1) The boundary conditions at x = 0 and x = L are called free-end conditions. Find the displacement u (x, t).
Transcribed Image Text:The longitudinal displacement of a vibrating elastic bar shown in the figure satisfies the wave a'u d'u equation a 0<x< L, t> 0 and the conditions: du du = 0, ax x L = 0, t> 0 ax x = 0 du u(x, 0) = x, = 0, 0 < x < L. t= 0 Hu(x, 1) The boundary conditions at x = 0 and x = L are called free-end conditions. Find the displacement u (x, t).
The longitudinal displacement of a vibrating elastic bar shown in the figure satisfies the wave a'u d'u equation a 0<x< L, t> 0 and the conditions: du du = 0, ax x L = 0, t> 0 ax x = 0 du u(x, 0) = x, = 0, 0 < x < L. t= 0 Hu(x, 1) The boundary conditions at x = 0 and x = L are called free-end conditions. Find the displacement u (x, t).
Transcribed Image Text:The longitudinal displacement of a vibrating elastic bar shown in the figure satisfies the wave a'u d'u equation a 0<x< L, t> 0 and the conditions: du du = 0, ax x L = 0, t> 0 ax x = 0 du u(x, 0) = x, = 0, 0 < x < L. t= 0 Hu(x, 1) The boundary conditions at x = 0 and x = L are called free-end conditions. Find the displacement u (x, t).
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