Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
az + A1 dt² — dt "xn(t)" = Aest S1 = + a。x = 0 −a₁ + √√a² − 4a₂a0 2a2 n(t) = A₁e³₁t + A₂e³₂t xn(t) = ? (a₂s² + a₁s + α₁) = 0 $2 -α₁ - √a² - 4a₂ª0 242 NATURAL RESPONSE, Xn Alest+A₂est (A₁+A₂t)e (A₁ cos wat+A₂ sin wat)e¯¤t

az + A1 dt² — dt "xn(t)" = Aest S1 = + a。x = 0 −a₁ + √√a² − 4a₂a0 2a2 n(t) = A₁e³₁t + A₂e³₂t xn(t) = ? (a₂s² + a₁s + α₁) = 0 $2 -α₁ - √a² - 4a₂ª0 242 NATURAL RESPONSE, Xn Alest+A₂est (A₁+A₂t)e (A₁ cos wat+A₂ sin wat)e¯¤t

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
See similar textbooks
icon
Related questions
Question
The complete response is the sum of the natural response and the forced response X = Xn+Xf Natural response of a first-order circuit Natural response of a second-order circuit CASE Overdamped Critically damped Underdamped az S1 = FORCING FUNCTION K Kt K₁² K sin cot Ke at Forced response of a first-order, or a second-order circuit + A₁ NATURAL FREQUENCIES $1,52 = -α± √√² - 0² $1,$₂=-α S1, S2 = -x±j√√/0²-a² -α±jood dx dt d²x dt² Solution of the Second-Order Differential Equation d²x x(t) = xn(t) + xf (t) a2 dt² + a。x = f(t) + A1 dx dt "xn(t)" = Aest Xn(t) = Ke-t/t + a。x = 0 -a₁ + √²-4a₂a0 242 - Xn(t) = A₁e³₁ª + A₂e³₂t ASSUMED RESPONSE A At + B At² +Bt+C A sin cot + B cos cot Ae-at NATURAL RESPONSE, Xn Ale+Azer (A₁+A₂t)e-at (A, cos coat+A₂ sin coat)e xn(t) = ? (a₂s² + a₁s+ao) = 0 -α₁ - √²-4a₂a0 242 NATURAL RESPONSE, Xn A₁ est + A₂e21 -α1 (A₁+A₂t)e (A₁ cos wat+A₂ sin wat)ext
Transcribed Image Text:The complete response is the sum of the natural response and the forced response X = Xn+Xf Natural response of a first-order circuit Natural response of a second-order circuit CASE Overdamped Critically damped Underdamped az S1 = FORCING FUNCTION K Kt K₁² K sin cot Ke at Forced response of a first-order, or a second-order circuit + A₁ NATURAL FREQUENCIES $1,52 = -α± √√² - 0² $1,$₂=-α S1, S2 = -x±j√√/0²-a² -α±jood dx dt d²x dt² Solution of the Second-Order Differential Equation d²x x(t) = xn(t) + xf (t) a2 dt² + a。x = f(t) + A1 dx dt "xn(t)" = Aest Xn(t) = Ke-t/t + a。x = 0 -a₁ + √²-4a₂a0 242 - Xn(t) = A₁e³₁ª + A₂e³₂t ASSUMED RESPONSE A At + B At² +Bt+C A sin cot + B cos cot Ae-at NATURAL RESPONSE, Xn Ale+Azer (A₁+A₂t)e-at (A, cos coat+A₂ sin coat)e xn(t) = ? (a₂s² + a₁s+ao) = 0 -α₁ - √²-4a₂a0 242 NATURAL RESPONSE, Xn A₁ est + A₂e21 -α1 (A₁+A₂t)e (A₁ cos wat+A₂ sin wat)ext
• Problem 2. Please solve the following circuit problems, as directed in the questions. (a) The current i(t) of the current source is shown in the figure (a). i(t) + i(t) ( 84 3H v(t) 4A 0 (a) Circuit A ■ Vin m Brief catalog of the Operational Amplifier circuits (Based on the ideal operational amplifier) R₁ V10M (a) Inverting amplifier R₁ U₂0-M -M R₁ Un m R₁ R₁ Ovout= R₁ www R₁ R₁ R₁ R₂2+ Vout=₁1+1 Vout R₁ Vin (d) Summing amplifier (1) What is the voltage of the inductor for t>0 ? where v(t) = 0, for t<0, and t > 8s t(s) 8s (2) How much is the energy stored in the capacitor for t>0? for Energy(t = 0) = 0 J Vin O R₁ R₁ -out (b) Noninverting amplifier R₂K1 U10-W R₂K₂ U20-W Ra/K3 R₁ + Vin R1 V30-W R₂/(1-(K₁ + K₂ + K3)) R(K4-1) Vin (c) Voltage follower (buffer amplifier) R₂ Ovout Vin Ovout K4(K₁v1 + K₂V2 + K303) (e) Noninverting summing amplifier
Transcribed Image Text:• Problem 2. Please solve the following circuit problems, as directed in the questions. (a) The current i(t) of the current source is shown in the figure (a). i(t) + i(t) ( 84 3H v(t) 4A 0 (a) Circuit A ■ Vin m Brief catalog of the Operational Amplifier circuits (Based on the ideal operational amplifier) R₁ V10M (a) Inverting amplifier R₁ U₂0-M -M R₁ Un m R₁ R₁ Ovout= R₁ www R₁ R₁ R₁ R₂2+ Vout=₁1+1 Vout R₁ Vin (d) Summing amplifier (1) What is the voltage of the inductor for t>0 ? where v(t) = 0, for t<0, and t > 8s t(s) 8s (2) How much is the energy stored in the capacitor for t>0? for Energy(t = 0) = 0 J Vin O R₁ R₁ -out (b) Noninverting amplifier R₂K1 U10-W R₂K₂ U20-W Ra/K3 R₁ + Vin R1 V30-W R₂/(1-(K₁ + K₂ + K3)) R(K4-1) Vin (c) Voltage follower (buffer amplifier) R₂ Ovout Vin Ovout K4(K₁v1 + K₂V2 + K303) (e) Noninverting summing amplifier
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Simplification of Boolean Functions Using Karnaugh Map
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS