The complete response is the sum of the natural response and the forced responseX = Xn+XfNatural response of a first-order circuitNatural response of a second-order circuitCASEOverdampedCritically dampedUnderdampedazS1 =FORCING FUNCTIONKKtK₁²K sin cotKe atForced response of a first-order, or a second-order circuit+ A₁NATURAL FREQUENCIES$1,52 = -α± √√² - 0²$1,$₂=-αS1, S2 = -x±j√√/0²-a² -α±jooddxdtd²xdt²Solution of the Second-Order Differential Equationd²xx(t) = xn(t) + xf (t)a2dt²+ a。x = f(t)+ A1dxdt"xn(t)" = AestXn(t) = Ke-t/t+ a。x = 0-a₁ + √²-4a₂a0242-Xn(t) = A₁e³₁ª + A₂e³₂tASSUMED RESPONSEAAt + BAt² +Bt+CA sin cot + B cos cotAe-atNATURAL RESPONSE, XnAle+Azer(A₁+A₂t)e-at(A, cos coat+A₂ sin coat)exn(t) = ?(a₂s² + a₁s+ao) = 0-α₁ - √²-4a₂a0242NATURAL RESPONSE, XnA₁ est + A₂e21-α1(A₁+A₂t)e(A₁ cos wat+A₂ sin wat)ext • Problem 5. The Circuit shown is at the steady state, before the switch is closed at time t=0Assume steady-state conditions exists.(For your knowledge, this might be an example, when a device is plugged into the power outletat the wall in the house.)vs (t) = 220 sin(100 t) (v)πVin mvs(t)R₁V10MUn(a) Derive the differential equation of i(t) over t for t≥ 0.(b) Find the forced response of i(t) over t for t≥ 0.(a) Find out the complete response of i(t) over t for t≥ 0.▪ Brief catalog of the Operational Amplifier circuits(Based on the ideal operational amplifier)(a) Inverting amplifierR₁U₂0-WR₂R₁wwwR₁Vout=-R₁ R₁Xot = 0R₁R₁Ovout R₁U₁+ ひntVin- VoutR₁Run)(d) Summing amplifier1HwwVinai(t)2HR₁.R₁.U10out(b) Noninverting amplifierU20R₂K1R₂/K₂R.K3+U30-WR₂/(1-(K₁ + K₂ + K3))5Ωww.VinRo(K4-1)0.5FRpVin O(c) Voltage follower (buffer amplifier)Ovout VinOvout K4(K₁v1 + K₂V₂ + K3V3)(e) Noninverting summing amplifier

Answered: Image /qna-images/answer/4e9238b9-72ce-467e-9249-9b393774f581.jpg

"xn(t)" = Aest S1 = -a₁ + √²-4a₂a0 2a2 xn(t) = A₁eS₁t + A₂eszt (a₂s² + a₁s + ao) = 0 S2 = -a₁-√²-4a₂a⁰ 2a2 NATURAL RESPONSE, Xn Alesit +A₂e21 (A₁+A₂t)e (A₁ cos wat+A₂ sin wat)e -αl

"xn(t)" = Aest S1 = -a₁ + √²-4a₂a0 2a2 xn(t) = A₁eS₁t + A₂eszt (a₂s² + a₁s + ao) = 0 S2 = -a₁-√²-4a₂a⁰ 2a2 NATURAL RESPONSE, Xn Alesit +A₂e21 (A₁+A₂t)e (A₁ cos wat+A₂ sin wat)e -αl

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...

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