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A string of length 15 cm is stretched between two points as shown in Figure 1. A point P on the string 5 cm from the point B is deflected a distance 5 cm from its position of rest perpendicular to AB and released with zero velocity. What are the initial conditions and boundary conditions for the problem? [Hint: initial conditions = u(x, 0) and ut(x, 0), boundary conditions u(0, t) and u(L, t)]. = Provided that the wave equation model for the problem mentioned above is utt 3uxx for (0 0). Compute the general displacement u(x, t) of any point at any time, t in seconds, for all cases using method of separation of variables. UA 5 10 15 Figure 1: Stretched string 0

A string of length 15 cm is stretched between two points as shown in Figure 1. A point P on the string 5 cm from the point B is deflected a distance 5 cm from its position of rest perpendicular to AB and released with zero velocity. What are the initial conditions and boundary conditions for the problem? [Hint: initial conditions = u(x, 0) and ut(x, 0), boundary conditions u(0, t) and u(L, t)]. = Provided that the wave equation model for the problem mentioned above is utt 3uxx for (0 0). Compute the general displacement u(x, t) of any point at any time, t in seconds, for all cases using method of separation of variables. UA 5 10 15 Figure 1: Stretched string 0

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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A string of length 15 cm is stretched between two points as shown in Figure 1. A point P on the string 5 cm from the point B is deflected a distance 5 cm from its position of rest perpendicular to AB and released with zero velocity. What are the initial conditions and boundary conditions for the problem? [Hint: initial conditions = u(x, 0) and ut(x, 0), boundary conditions = u(0, t) and u(L, t)]. Provided that the wave equation model for the problem mentioned above is utt = 3uxx for (0<x<L, t> 0). Compute the general displacement u(x, t) of any point at any time, t in seconds, for all cases using method of separation of variables. u 10 15 Figure 1: Stretched string LO 5 0 A B
Transcribed Image Text:A string of length 15 cm is stretched between two points as shown in Figure 1. A point P on the string 5 cm from the point B is deflected a distance 5 cm from its position of rest perpendicular to AB and released with zero velocity. What are the initial conditions and boundary conditions for the problem? [Hint: initial conditions = u(x, 0) and ut(x, 0), boundary conditions = u(0, t) and u(L, t)]. Provided that the wave equation model for the problem mentioned above is utt = 3uxx for (0<x<L, t> 0). Compute the general displacement u(x, t) of any point at any time, t in seconds, for all cases using method of separation of variables. u 10 15 Figure 1: Stretched string LO 5 0 A B
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