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# Solved: Consider an elastic string of length L whose ends are held fixed. The string is ISBN: 9780470383346 394

## Solution for problem 4 Chapter 10.7

Elementary Differential Equations and Boundary Value Problems | 9th Edition

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Problem 4

Consider an elastic string of length L whose ends are held fixed. The string is set in motion with no initial velocity from an initial position u(x, 0) = f(x). In each of 1 through 4 carry out the following steps. Let L = 10 and a = 1 in parts (b) through (d). (a) Find the displacement u(x, t) for the given initial position f(x). (b) Plot u(x, t) versus x for 0 x 10 and for several values of t between t = 0 and t = 20. (c) Plot u(x, t) versus t for 0 t 20 and for several values of x. (d) Construct an animation of the solution in time for at least one period. (e) Describe the motion of the string in a few sentences.f(x) =1, L/2 1 < x < L/2 + 1 (L > 2),0, otherwise

Step-by-Step Solution:
Step 1 of 3

Here is the definition of the logarithm function. If b is any number such that and and then, We usually read this as “log base b of x”. In this definition is called the logarithm form and is called the exponential form. Note that the requirement that is really a result of the fact that we are also requiring . If you think about it, it will make sense. We are raising a positive number to an exponent and so there is no way that the result can possibly be anything other than another positive number. It is very important to remember that we can’t take the logarithm of zero or a negative number. Now, let’

Step 2 of 3

Step 3 of 3

##### ISBN: 9780470383346

Elementary Differential Equations and Boundary Value Problems was written by and is associated to the ISBN: 9780470383346. The full step-by-step solution to problem: 4 from chapter: 10.7 was answered by , our top Math solution expert on 03/13/18, 08:22PM. Since the solution to 4 from 10.7 chapter was answered, more than 265 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Elementary Differential Equations and Boundary Value Problems, edition: 9. The answer to “Consider an elastic string of length L whose ends are held fixed. The string is set in motion with no initial velocity from an initial position u(x, 0) = f(x). In each of 1 through 4 carry out the following steps. Let L = 10 and a = 1 in parts (b) through (d). (a) Find the displacement u(x, t) for the given initial position f(x). (b) Plot u(x, t) versus x for 0 x 10 and for several values of t between t = 0 and t = 20. (c) Plot u(x, t) versus t for 0 t 20 and for several values of x. (d) Construct an animation of the solution in time for at least one period. (e) Describe the motion of the string in a few sentences.f(x) =1, L/2 1 < x < L/2 + 1 (L > 2),0, otherwise” is broken down into a number of easy to follow steps, and 144 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 75 chapters, and 1990 solutions.

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Solved: Consider an elastic string of length L whose ends are held fixed. The string is