barcode print in asp net CHAP. 31 in Visual Studio .NET

Making Denso QR Bar Code in Visual Studio .NET CHAP. 31

CHAP. 31
QR Code Scanner In Visual Studio .NET
Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in Visual Studio .NET applications.
Drawing QR Code In .NET
Using Barcode generator for .NET Control to generate, create QR image in VS .NET applications.
LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS
QR Code Decoder In VS .NET
Using Barcode reader for VS .NET Control to read, scan read, scan image in .NET applications.
Encoding Barcode In VS .NET
Using Barcode maker for .NET Control to generate, create barcode image in Visual Studio .NET applications.
Using Eq. (3.441, we have SX,(S) -x(o-)
Barcode Recognizer In VS .NET
Using Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in VS .NET applications.
QR Maker In Visual C#
Using Barcode creator for .NET framework Control to generate, create QR Code 2d barcode image in .NET framework applications.
k(') / m-e-" dt
Make QR Code In .NET
Using Barcode drawer for ASP.NET Control to generate, create QR Code JIS X 0510 image in ASP.NET applications.
QR Code JIS X 0510 Generator In VB.NET
Using Barcode encoder for VS .NET Control to generate, create QR Code image in VS .NET applications.
= /O'd'oe-s'dt
Painting Bar Code In Visual Studio .NET
Using Barcode printer for .NET framework Control to generate, create barcode image in VS .NET applications.
Draw GTIN - 13 In VS .NET
Using Barcode creator for .NET Control to generate, create EAN / UCC - 13 image in .NET framework applications.
e-st
Paint UCC - 12 In VS .NET
Using Barcode printer for .NET framework Control to generate, create GTIN - 128 image in VS .NET applications.
Making 2 Of 5 Interleaved In .NET
Using Barcode creator for .NET framework Control to generate, create ANSI/AIM I-2/5 image in VS .NET applications.
W t ) e -" dt
Encode UPC-A Supplement 5 In Objective-C
Using Barcode generator for iPad Control to generate, create UPC A image in iPad applications.
GTIN - 128 Creation In VS .NET
Using Barcode drawer for Reporting Service Control to generate, create EAN 128 image in Reporting Service applications.
/o+ - dt dt =x(O+) - x ( o - ) + / - W f ) e-s,dt o+ dt
Paint Bar Code In VB.NET
Using Barcode generation for .NET Control to generate, create bar code image in Visual Studio .NET applications.
Making Code 39 Full ASCII In Visual C#.NET
Using Barcode printer for Visual Studio .NET Control to generate, create ANSI/AIM Code 39 image in Visual Studio .NET applications.
=x(t)E + Thus,
Creating Data Matrix 2d Barcode In None
Using Barcode encoder for Font Control to generate, create Data Matrix image in Font applications.
Linear 1D Barcode Generator In Visual Studio .NET
Using Barcode printer for ASP.NET Control to generate, create Linear Barcode image in ASP.NET applications.
lirn sX,(s) =x(O+) +
GTIN - 13 Decoder In C#
Using Barcode decoder for .NET framework Control to read, scan read, scan image in .NET applications.
Creating ANSI/AIM Code 128 In None
Using Barcode encoder for Office Word Control to generate, create Code 128A image in Microsoft Word applications.
5-07
since lim, ,, e-" = 0. ( b ) Again using Eq. (3.441, we have lirn [sX,(s) - x(0-)]
( / a & dtt ) ePS'dt 0-
lirn e-"'
lirn x(t ) - ~ ( 0 ~ )
t-rm
Since we conclude that
s-ro
lirn [sX,(s) -x(0-)]
s-ro
lim [sx,(s)] -x(O-)
limx(t)
t--t-
lirnsX,(s)
s-ro
3.36. T h e unilateral Laplace transform is sometimes defined as
' with O+ as the lower limit. (This definition is sometimes referred to as the 0 definition.)
( a ) Show that
LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS
[CHAP. 3
( b ) Show that
Let x ( t ) have unilateral Laplace transform X, (s). Using Eq. (3.99) and integrating by parts, we obtain
Thus, we have
( b ) By definition (3.99)
P+{u(t)) =
,/' u ( t ) e - " d t = ,/ e-"dt 0
Re(s) > 0
From Eq. (1.30)we have
Taking the 0' unilateral Laplace transform of Eq. (3.103) and using Eq. (3.100), we obtain
This is consistent with Eq. (1.21);that is,
Note that taking the 0 unilateral Laplace transform of Eq. (3.103)and using Eq. (3.44), we obtain
APPLICATION OF UNILATERAL LAPLACE TRANSFORM 337. Using the unilateral Laplace transform, redo Prob. 2.20.
The system is described by
~ ' ( t ) ay(t)= x ( l ) +
with y(0) = yo and x(t
e - ~ 'tu ( 1.
CHAP. 31
LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS
Assume that y(0) = y(0-1. Let ~ ( t-Y,(s) ) Then from Eq. (3.44) y l ( t )-sY,(s) From Table 3-1 we have x ( t )-X,(S)
-y(O-) =sY,(s) - Y o
R e ( s ) > -b
Taking the unilateral Laplace transform of Eq. (3.1041,we obtain
or Thus, Y1(s)=
K (s+a)(s+b)
Using partial-fraction expansions, we obtain
Taking the inverse Laplace transform of Y,(s),we obtain y ( t ) = yoe-"+ -( e - b r - e - a : ) a-b which is the same as Eq. (2.107). Noting that y(O+) = y(0) = y(0-) = yo, we write y ( t ) as y ( t ) = y0e-O1 +
-( e - b r
- e-a')
3.38. Solve the second-order linear differential equation
y"(t)
+ 5 y 1 ( t )+ 6 y ( t ) = x ( t )
with the initial conditions y(0) = 2, yl(0) = 1 and x ( t ) = e P ' u ( t ) . ,
Assume that y(0) = y(0-) and yl(0)= yl(O-). Let ~ ( t-Y,(s) ) Then from Eqs. (3.44) and (3.45)
yN(t) From Table 3-1 we have
y l ( t ) -sY,(s)
- y ( 0 - ) = s Y , ( s )- 2
=s2YJs)-
s2Y1(s)- sy(0-) - y l ( O - )
2s - I
LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS
[CHAP. 3
Taking the unilateral Laplace transform of Eq. (3.105),we obtain
Thus,
Using partial-fraction expansions, we obtain
Taking the inverse Laplace transform of Yl(s),we have Notice that y(O+) = 2 = y(O) and y'(O+)= 1 = yl(0);and we can write y ( f ) as
3.39. Consider t h e RC circuit shown in Fig. 3-14(a). T h e switch is closed at t that there is a n initial voltage o n the capacitor and uC(Om) u,,. =
( a ) Find the current i ( t ) .
Assume
( 6 ) Find the voltage across the capacitor u c ( t ) .
vc (0)=v,
Fig. 3-14 RC circuit.
( a ) With the switching action, the circuit shown in Fig. 3-14(a) can be represented by the = circuit shown in Fig. 3-14(b)with i.f,(t) Vu(t).When the current i ( t ) is the output and the input is r,(t), the differential equation governing the circuit is 1 (3.106) Ri(t) + i ( r ) d~ = c s ( t ) C , Taking the unilateral Laplace transform of Eq. (3.106) and using Eq. (3.481, we obtain
CHAP. 31
LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS
Now and Hence, Eq. (3.107) reduces to
( t )= -
i ( r )dr C ,
Solving for I(s), we obtain
I(s) =
v-0,
1 R + 1/Cs
v-u, R s
1 + l/RC
Taking the inverse Laplace transform of I(s), we get
( b ) When u,(r) is the output and the input is u,(t), the differential equation governing the circuit is
Taking the unilateral Laplace transform of Eq. (3.108) and using Eq. (3.441, we obtain
Solving for V,(s),we have
v 1 V c ( s )= RCs(s+l/RC)
+ s + luoR C /
Taking the inverse Laplace transform of I/,(s), we obtain
u c ( t )= V [ 1- e - t / R C ] u ( t ) ~ , e - ' / ~ ~ u ( t ) +
Note that uc(O+)= u,
= u,(O-).
Thus, we write uc(t) as
u c ( t ) = V ( 1 -e-'IRC)
~ e - ' / t~r O ~
3.40. Using the transform network technique, redo Prob. 3.39.
Using Fig. 3-10, the transform network corresponding to Fig. 3-14 is constructed as shown in Fig. 3-15.
LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS
[CHAP. 3
Fig. 3-15 Transform circuit, Writing the voltage law for the loop, we get
Solving for I(s), we have
v-u, 1 v-u, 1 -I(s)= s R + 1/Cs R s + l/RC
Taking the inverse Laplace transform of I(s), we obtain
( b ) From Fig.3.15 we have
Substituting I ( s ) obtained in part (a) into the above equation, we get
Taking the inverse Laplace transform of V,(s),we have
3.41. In the circuit in Fig. 3-16(a) the switch is in the closed position for a long time before it is opened at t = 0. Find the inductor current i(t) for t 2 0.
When the switch is in the closed position for a long time, the capacitor voltage is charged to 10 V and there is no current flowing in the capacitor. The inductor behaves as a short circuit, and the inductor current is = 2 A. Thus, when the switch is open, we have i ( O - ) = 2 and u,(O-) = 10; the input voltage is 10 V, and therefore it can be represented as lOu(t). Next, using Fig. 3-10, we construct the transform circuit as shown in Fig. 3-16(b).
Copyright © OnBarcode.com . All rights reserved.