Consider the electric circuit illustrated below. Let I be the current through the inductor and V be the voltage across the capacitor. Then I and V satisfy the linear system: L IP dt R1 I + ()► V R1 R2 (). dV 1 I + V CR2 dt C Let R1 = 10, R2 -n, L – 2 H, and C = - F. Answer the following questions about the system: (a) Express the system in matrix notation: T = PF (). (b) Verify that = is an eigenvector of P. Identify the corresponding eigenvalue A1. (c) Given that12 = -2 is an eigenvalue of P, identify an eigenvector 2 that corresponds to X2. (d) Find the general solution to the system of differential equations. (e) Show that I(t) + 0 and V(t) → 0 as t → 0, regardless of the initial values of I(0) and V(0).
Consider the electric circuit illustrated below. Let I be the current through the inductor and V be the voltage across the capacitor. Then I and V satisfy the linear system: L IP dt R1 I + ()► V R1 R2 (). dV 1 I + V CR2 dt C Let R1 = 10, R2 -n, L – 2 H, and C = - F. Answer the following questions about the system: (a) Express the system in matrix notation: T = PF (). (b) Verify that = is an eigenvector of P. Identify the corresponding eigenvalue A1. (c) Given that12 = -2 is an eigenvalue of P, identify an eigenvector 2 that corresponds to X2. (d) Find the general solution to the system of differential equations. (e) Show that I(t) + 0 and V(t) → 0 as t → 0, regardless of the initial values of I(0) and V(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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Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
Need parts c, d and e please
![6.
Consider the electric circuit illustrated below. Let I be the current through the inductor
and V be the voltage across the capacitor. Then I and V satisfy the linear system:
L
IP
dt
R1
I +
L
().
V
R1
R2
AP
dt
1
I +
V
CR2
Let R1
1N, R2 = N, L = 2 H, and C = ? F. Answer the following questions about the system:
(a) Express the system in matrix notation:
T' = Pa
(6)
(b) Verify that ī =
is an eigenvector of P. Identify the corresponding eigenvalue A1.
(c) Given that A2
= -2 is an eigenvalue of P, identify an eigenvector 2 that corresponds to A2.
(d) Find the general solution to the system of differential equations.
(e) Show that I(t)
→ 0 and V (t) → 0 as t → ∞, regardless of the initial values of I(0) and V(0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a8e0411-af3c-4fe9-9f60-29bf0a08ded5%2F122da41c-0f9b-471a-ab7a-a4f91a5703d0%2Fiuopzz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6.
Consider the electric circuit illustrated below. Let I be the current through the inductor
and V be the voltage across the capacitor. Then I and V satisfy the linear system:
L
IP
dt
R1
I +
L
().
V
R1
R2
AP
dt
1
I +
V
CR2
Let R1
1N, R2 = N, L = 2 H, and C = ? F. Answer the following questions about the system:
(a) Express the system in matrix notation:
T' = Pa
(6)
(b) Verify that ī =
is an eigenvector of P. Identify the corresponding eigenvalue A1.
(c) Given that A2
= -2 is an eigenvalue of P, identify an eigenvector 2 that corresponds to A2.
(d) Find the general solution to the system of differential equations.
(e) Show that I(t)
→ 0 and V (t) → 0 as t → ∞, regardless of the initial values of I(0) and V(0).
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