Solve part b. of question 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Solve part b. of question 2.
![# Problems
In each of Problems 1 through 8:
a. Sketch the graph of the forcing function on an appropriate interval.
b. Find the solution of the given initial value problem.
c. Plot the graph of the solution.
d. Explain how the graphs of the forcing function and the solution are related.
1. \( y'' + y = f(t); \quad y(0) = 0, \quad y'(0) = 1; \)
\[
f(t) =
\begin{cases}
1, & 0 \leq t < 3\pi \\
0, & 3\pi \leq t < \infty
\end{cases}
\]
2. \( y'' + 2y' + 2y = h(t); \quad y(0) = 0, \quad y'(0) = 1; \)
\[
h(t) =
\begin{cases}
1, & \pi \leq t < 2\pi \\
0, & 0 \leq t < \pi \quad \text{or} \quad t \geq 2\pi
\end{cases}
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Transcribed Image Text:# Problems
In each of Problems 1 through 8:
a. Sketch the graph of the forcing function on an appropriate interval.
b. Find the solution of the given initial value problem.
c. Plot the graph of the solution.
d. Explain how the graphs of the forcing function and the solution are related.
1. \( y'' + y = f(t); \quad y(0) = 0, \quad y'(0) = 1; \)
\[
f(t) =
\begin{cases}
1, & 0 \leq t < 3\pi \\
0, & 3\pi \leq t < \infty
\end{cases}
\]
2. \( y'' + 2y' + 2y = h(t); \quad y(0) = 0, \quad y'(0) = 1; \)
\[
h(t) =
\begin{cases}
1, & \pi \leq t < 2\pi \\
0, & 0 \leq t < \pi \quad \text{or} \quad t \geq 2\pi
\end{cases}
\]
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