Suppose a mechanical oscillator obeys the IVP y" + 4y' + 5y = 0 y(0) = 0, y'(0) = 1 (1) Note: Write your vectors so that, if it is a constant vector, the first element is 1.To enter a 1 vector, separate each entry by a comma. For example,3 should be entered as " (1,2*e^(3*t))". Write exponential eat as "e^(a*t)". (a) Write this as a first-order vector IVP, that is, an IVP of the form æ' = A |æ(0) = a (2) where A is a constant 2 x 2 matrix and a is a constant vector.
Suppose a mechanical oscillator obeys the IVP y" + 4y' + 5y = 0 y(0) = 0, y'(0) = 1 (1) Note: Write your vectors so that, if it is a constant vector, the first element is 1.To enter a 1 vector, separate each entry by a comma. For example,3 should be entered as " (1,2*e^(3*t))". Write exponential eat as "e^(a*t)". (a) Write this as a first-order vector IVP, that is, an IVP of the form æ' = A |æ(0) = a (2) where A is a constant 2 x 2 matrix and a is a constant vector.
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
![Suppose a mechanical oscillator obeys the IVP
(y" + 4y' + 5y = 0
(1)
| y(0) = 0, y'(0) = 1
Note: Write your vectors so that, if it is a constant vector, the first element is 1.To enter a
1
vector, separate each entry by a comma. For example,
should be entered as "
3t
(1,2*e^(3*t))". Write exponential eat as "e^(a*t)".
(a) Write this as a first-order vector IVP, that is, an IVP of the form
æ' = Ax
(0) = a
(2)
where A is a constant 2 × 2 matrix and a is a constant vector.
a11 a12]
where a1l=
Answer: A =
Number
, a12=
Number
, a21=
[a21 а22.
Number
, а22—
Number
and a =
Number
Number
).
(b) Find the solution to (2), hence write down the solution to (1).
Answer: æ(t) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1e46184-5bb3-4339-852b-bb3ef2e0784b%2F82e178e8-a53f-4e04-a7af-294aa750b61f%2Fpaprd7_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose a mechanical oscillator obeys the IVP
(y" + 4y' + 5y = 0
(1)
| y(0) = 0, y'(0) = 1
Note: Write your vectors so that, if it is a constant vector, the first element is 1.To enter a
1
vector, separate each entry by a comma. For example,
should be entered as "
3t
(1,2*e^(3*t))". Write exponential eat as "e^(a*t)".
(a) Write this as a first-order vector IVP, that is, an IVP of the form
æ' = Ax
(0) = a
(2)
where A is a constant 2 × 2 matrix and a is a constant vector.
a11 a12]
where a1l=
Answer: A =
Number
, a12=
Number
, a21=
[a21 а22.
Number
, а22—
Number
and a =
Number
Number
).
(b) Find the solution to (2), hence write down the solution to (1).
Answer: æ(t) =
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