Consider the following initial value problem: y" + 9y = 38(t – T); y(0) = 0, y'(0) = 0 %3D a) Find the solution y(t). NOTE: Denote the Heaviside function by uc(t) where uc(t) = 1 if t > c and 0 otherwise. Indicate separately the value of c. y(t) where c = b) Use a graphing utility to plot the solution y(t).
Consider the following initial value problem: y" + 9y = 38(t – T); y(0) = 0, y'(0) = 0 %3D a) Find the solution y(t). NOTE: Denote the Heaviside function by uc(t) where uc(t) = 1 if t > c and 0 otherwise. Indicate separately the value of c. y(t) where c = b) Use a graphing utility to plot the solution y(t).
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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![### Initial Value Problem
Consider the following initial value problem:
\[ y'' + 9y = 3\delta(t - \pi); \quad y(0) = 0, \quad y'(0) = 0 \]
#### a) Find the solution \( y(t) \).
**NOTE:** Denote the Heaviside function by \( u_c(t) \) where \( u_c(t) = 1 \) if \( t \geq c \) and 0 otherwise. Indicate separately the value of \( c \).
\[ y(t) = \boxed{\phantom{fill in the solution}} \]
where \( c = \boxed{\phantom{fill in the value of c}} \)
#### b) Use a graphing utility to plot the solution \( y(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4bdfca1-c479-4089-8b74-947c8fb213c2%2F8731c632-9f98-403c-b94e-70597101bedb%2Fjmfiadj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Initial Value Problem
Consider the following initial value problem:
\[ y'' + 9y = 3\delta(t - \pi); \quad y(0) = 0, \quad y'(0) = 0 \]
#### a) Find the solution \( y(t) \).
**NOTE:** Denote the Heaviside function by \( u_c(t) \) where \( u_c(t) = 1 \) if \( t \geq c \) and 0 otherwise. Indicate separately the value of \( c \).
\[ y(t) = \boxed{\phantom{fill in the solution}} \]
where \( c = \boxed{\phantom{fill in the value of c}} \)
#### b) Use a graphing utility to plot the solution \( y(t) \).
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