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barcode reader using vb net source code Figure 545 Response of underdamped secondorder circuit in Software
Figure 545 Response of underdamped secondorder circuit Denso QR Bar Code Scanner In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. QR Code Drawer In None Using Barcode maker for Software Control to generate, create QR Code image in Software applications. As a nal note, we return to the special situation in Case III when R is identically zero We de ned this earlier as the resonance condition The resonant solution is not characterized by an exponential decay (damping), and gives rise to a pure sinusoidal waveform, oscillating at the natural frequency, Resonant circuits nd application in lters, which are presented in 6 We shall not discuss this case any longer in the present chapter Forced and Complete Response of SecondOrder Circuits Once we obtain the natural response using the techniques described in the preceding section, we may nd the forced response using the same method employed for rstorder circuits Once again, we shall limit our analysis to a switched DC forcing Reading Denso QR Bar Code In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. Draw Denso QR Bar Code In C#.NET Using Barcode drawer for .NET Control to generate, create QR Code ISO/IEC18004 image in .NET framework applications. Part I
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Painting QR In VB.NET Using Barcode generator for .NET Control to generate, create QR Code ISO/IEC18004 image in .NET framework applications. Code 128A Encoder In None Using Barcode encoder for Software Control to generate, create Code 128A image in Software applications. function, for the sake of simplicity (the form of the forced response when the forcing function is a switched sinusoid is explored in the homework problems) The form of the forced differential equation is a d 2 x(t) dx(t) +b + cx(t) = F dt 2 dt (573) DataMatrix Creation In None Using Barcode encoder for Software Control to generate, create Data Matrix image in Software applications. UPCA Supplement 5 Creation In None Using Barcode generator for Software Control to generate, create UCC  12 image in Software applications. where F is a constant Therefore we assume a solution of the form xF (t) = XF = constant, and we substitute in the forced equation to nd that XF = F c (574) Printing EAN 128 In None Using Barcode encoder for Software Control to generate, create UCC  12 image in Software applications. Encoding GTIN  13 In None Using Barcode drawer for Software Control to generate, create EAN13 image in Software applications. Finally, in order to compute the complete solution, we sum the natural and forced responses, to obtain x(t) = xN (t) + xF (t) = K1 es1 t + K2 es2 t + F c (575) Identcode Generation In None Using Barcode generator for Software Control to generate, create Identcode image in Software applications. Create Code 128 Code Set C In Java Using Barcode encoder for Java Control to generate, create Code 128C image in Java applications. For a secondorder differential equation, we need two initial conditions to solve for the constants K1 and K2 These are the values of x(t) at t = 0 and of the derivative of x(t), dx/dt, at t = 0 To complete the solution, we therefore need to solve the two equations x(t = 0) = x0 = K1 + K2 + and dx (t = 0) = x0 = s1 K1 + s2 K2 dt (577) F c (576) Code128 Scanner In Visual C#.NET Using Barcode reader for VS .NET Control to read, scan read, scan image in .NET applications. Making Code 128 Code Set B In VS .NET Using Barcode generation for ASP.NET Control to generate, create ANSI/AIM Code 128 image in ASP.NET applications. To summarize, we must follow the steps in the accompanying methodology box to obtain the complete solution of a secondorder circuit excited by a switched DC source Code 128C Creation In Java Using Barcode generation for Java Control to generate, create Code 128B image in Java applications. GS1  13 Printer In ObjectiveC Using Barcode creation for iPad Control to generate, create EAN13 image in iPad applications. F O C U S O N M E T H O D O L O G Y
Encode UPCA Supplement 2 In ObjectiveC Using Barcode drawer for iPhone Control to generate, create GTIN  12 image in iPhone applications. Make Code 128B In None Using Barcode generator for Online Control to generate, create USS Code 128 image in Online applications. Solution of SecondOrder Circuits 1 Write the differential equation for the circuit 2 Find the roots of the characteristic polynomial, and determine the natural response 3 Find the forced response 4 Write the complete solution as the sum of natural and forced responses 5 Determine the initial conditions for inductor currents and capacitor voltages 6 Apply the initial conditions to the complete solution to determine the constants K1 and K2 Although these steps are straightforward, the successful application of this technique will require some practice, especially the determination of the initial conditions and the computation of the constants There is no substitute for practice in gaining familiarity with these techniques! The following examples should be of help in illustrating the methods just described 5
Transient Analysis
EXAMPLE 510 Complete Response of Overdamped SecondOrder Circuit
Problem
t=0 + vC(t) _ C
Determine the complete response of the circuit of Figure 546
+ vR(t) _ +
Solution
i(t) vL(t) _ Known Quantities: Resistor, capacitor, inductor values; source voltage Find: The capacitor voltage as a function of time R = 5000 L = 1 H C = 1 F VS = 25 V
Vs = 25 V
Schematics, Diagrams, Circuits, and Given Data: R = 5 k ; C = 1 F; L = 1 H; Assumptions: The capacitor has been charged (through a separate circuit, not shown) prior to the switch closing, such that vC (0) = 5 V Analysis: 1 Apply KVL to determine the circuit differential equation: VS vC (t) vR (t) vL (t) = 0 VS
t idt iR L
di =0 dt
R di 1 1 dVS d i + + i= =0 t >0 dt 2 L dt LC L dt We note that the above equations that we have chosen the series (inductor) current as the variable in the differential equation; we also observe that the DC forcing function is zero, because the capacitor acts as an open circuit in the steady state, and the current will therefore be zero as t 2 We determine the characteristic polynomial by substituting s for d/dt: s2 + 1 R s+ =0 L LC 1 L 2R 2 R L s1,2 =

