Consider the initial value problem for function y given by. y"-y-12y=4u(t) sin(21). where u(t-c) denotes the step function with step at t = c. y(0) = 0, y (0) = 0.
Consider the initial value problem for function y given by. y"-y-12y=4u(t) sin(21). where u(t-c) denotes the step function with step at t = c. y(0) = 0, y (0) = 0.
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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![Consider the initial value problem for function y given by,
where u(t-c) denotes the step function with step at t = c.
y"-y-12y=4u(t) sin(21). y(0) = 0,
Part 1: Finding F(x)
- Part 2: Finding Y (s)
(b) Find the Laplace Transform of the solution, Y(s) = a[y()].
Y(s) = -8e^(-pi s/2)/(s^2+4)(-4)(3+3))
Note: We are asking for the Laplace Transform of the solution, Y (s), not for the solution y(t).
Part 3: Rewriting Y (8)
- Part 4: Finding y(t)
(d) Use the expresion of Y (s) found in (b) to write the solution y(t) as
Yn (t)=
y(t) = Aya(t) + Bys(t) + Cyc()+DYp (1).
where A, B, C, D are the same constants found in the previous part. Find the functions ya. Ya. yc. YD.
YA (t) =
Σ
Ye(t)=
YD (t)=
Σ
M
y (0) = 0.
Σ](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ed5ea57-5dda-4ad5-9230-267038297200%2F30464b01-87a0-417d-8733-a5efdd322b28%2Fw1l5rk5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem for function y given by,
where u(t-c) denotes the step function with step at t = c.
y"-y-12y=4u(t) sin(21). y(0) = 0,
Part 1: Finding F(x)
- Part 2: Finding Y (s)
(b) Find the Laplace Transform of the solution, Y(s) = a[y()].
Y(s) = -8e^(-pi s/2)/(s^2+4)(-4)(3+3))
Note: We are asking for the Laplace Transform of the solution, Y (s), not for the solution y(t).
Part 3: Rewriting Y (8)
- Part 4: Finding y(t)
(d) Use the expresion of Y (s) found in (b) to write the solution y(t) as
Yn (t)=
y(t) = Aya(t) + Bys(t) + Cyc()+DYp (1).
where A, B, C, D are the same constants found in the previous part. Find the functions ya. Ya. yc. YD.
YA (t) =
Σ
Ye(t)=
YD (t)=
Σ
M
y (0) = 0.
Σ
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