Question

2. Consider and elastic string of length 10 whose ends are held fixed. The string is set in motion with no initial velocity from an initial position $u(x, 0) = f(x)$, where \\ $f(x) = \begin{cases} x/5 & \text{if } 0 \le x \le 5, \\ (10 - x)/5 & \text{if } 5 < x \le 10. \end{cases}$ \\ Find $u(x, t)$ (Assume $a = 1$.)

          2. Consider and elastic string of length 10 whose ends are held fixed. The string is set in motion with no initial velocity from an initial position $u(x, 0) = f(x)$, where \\
$f(x) = \begin{cases} x/5 & \text{if } 0 \le x \le 5, \\ (10 - x)/5 & \text{if } 5 < x \le 10. \end{cases}$ \\
Find $u(x, t)$ (Assume $a = 1$.)

2. Consider and elastic string of length 10 whose ends are held fixed. The string is set in motion with no initial velocity from an initial position u(x, 0) = f(x), where

f(x) = x/5 if 0 ≤ x ≤ 5,
(10 - x)/5 if 5 < x ≤ 10.

Find u(x, t) (Assume a = 1.)

Added by Elisa G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shyam P

04/19/2022

Step 1

Step 1: We are given the initial position of the string, u0 = f, which is defined as: u(x, t) = (x/5) if 0 ≤ x ≤ 5, and u(x, t) = 10 - (x/5) if 5 < x ≤ 10. Show more…

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2. Consider a clastic string of length 10 whose ends are held fixed. The string is set in motion with no initial velocity from an initial position u0 = f where u(x, t) = (x/5) if 0 ≤ x ≤ 5, and u(x, t) = 10 - (x/5) if 5 < x ≤ 10. Find u(x, t). (Assume 1 ≤ t ≤ 11)