2. Solve Utt- c²UTT for x = [0, π] with the boundary conditions and the initial conditions = 0 U₂ (0, t) = U₂(π, t) = 0 U(x,0) = 0, Ut(x,0) = cos²x.
2. Solve Utt- c²UTT for x = [0, π] with the boundary conditions and the initial conditions = 0 U₂ (0, t) = U₂(π, t) = 0 U(x,0) = 0, Ut(x,0) = cos²x.
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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Question
Question 2 and 4 only please
![2. Solve
for r [0, π] with the boundary conditions
and the initial conditions
Utt- c²Uzz = 0
Hint:
U₂ (0, t) = U₂(T, t) = 0
U(x,0) = 0,
U₁(x, 0) = cos²x.
• cos²x =
cos(2x)+1
=
• Also notice the boundary conditions for this question, compared to the one U(0, t)
U(L, t) = 0 in the lecture notes, and the one U₂(0, t) = U(L, t) = 0 from Question 1.
3. Find the Fourier series of f(x) = |x| on [-L, L]. Draw a sketch of f(x).
4. Find the Fourier series of f(x) = | sin x on the interval [-, π]. Draw a sketch of f(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdddfff36-bd46-4e8f-b66f-7a4677280cea%2F5254ca53-f11e-4e5a-b0cb-992a54df6812%2Fsfwc8wm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Solve
for r [0, π] with the boundary conditions
and the initial conditions
Utt- c²Uzz = 0
Hint:
U₂ (0, t) = U₂(T, t) = 0
U(x,0) = 0,
U₁(x, 0) = cos²x.
• cos²x =
cos(2x)+1
=
• Also notice the boundary conditions for this question, compared to the one U(0, t)
U(L, t) = 0 in the lecture notes, and the one U₂(0, t) = U(L, t) = 0 from Question 1.
3. Find the Fourier series of f(x) = |x| on [-L, L]. Draw a sketch of f(x).
4. Find the Fourier series of f(x) = | sin x on the interval [-, π]. Draw a sketch of f(x).
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