Need parts c, d and e please 6.Consider the electric circuit illustrated below. Let I be the current through the inductorand V be the voltage across the capacitor. Then I and V satisfy the linear system:LIPdtR1I +L().VR1R2APdt1I +VCR2Let R11N, 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).

Given :- The electric circuit illustrated as : dIdt = -R1L I + - 1L VdVdt = 1C I + - 1CR2 V

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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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

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).

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