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d'u =16- for all 0sxs10 and t20

d'u =16- for all 0sxs10 and t20

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Wave mechanics are often employed for the analysis of piles during impact driving. The 1-dimensional wave equation can be used to investigate the bearing capacity resistance of a pile foundation. Assume that at time t= 0, the displacement due to vibration of a pile of length 10m is zero, while the rate of change of its displacement is uniform at 20m/s. The 1-dimensional wave equation used in the investigation is given as follows: d'u =16- for all 0<x<10 and t20 (a) Describe the initial and boundary conditions of the wave equation in this scenario. (b) Hence, deduce the displacement function u(x,t) of the pile, subject to the conditions in (a).
Transcribed Image Text:Wave mechanics are often employed for the analysis of piles during impact driving. The 1-dimensional wave equation can be used to investigate the bearing capacity resistance of a pile foundation. Assume that at time t= 0, the displacement due to vibration of a pile of length 10m is zero, while the rate of change of its displacement is uniform at 20m/s. The 1-dimensional wave equation used in the investigation is given as follows: d'u =16- for all 0<x<10 and t20 (a) Describe the initial and boundary conditions of the wave equation in this scenario. (b) Hence, deduce the displacement function u(x,t) of the pile, subject to the conditions in (a).
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