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}{TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 12 "Mod de lucru" }
}{PARA 0 "" 0 "" {TEXT -1 133 "In afara de functiile incluse in librar
ia standard Maple, in aceasta lucrare vor fi utilizate cateva functii \+
din libraria aditionala " }{TEXT 258 7 "SCSlib." }}{PARA 0 "" 0 "" 
{TEXT -1 73 "Pentru calcularea si reprezentarea singularitatilor funct
iei de transfer:" }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " }{TEXT 259 
71 "PZ[numeric]                                                       \+
     " }{HYPERLNK 17 "help" 1 "..\\Help\\Helpfile.mws" "Functia PZ[num
eric]" }{TEXT -1 1 " " }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " }
{TEXT 260 74 "PZ[grafic]                                              \+
                  " }{HYPERLNK 17 "help" 1 "..\\Help\\Helpfile.mws" "F
unctia PZ[grafic]" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 29 "libname:=\"../SCSlib\",libname:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(inttrans):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 32 "addtable(laplace,e(t),E(s),t,s):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "addtable(laplace,y(t),Y(s),t
,s):" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 53 "Ecuatie diferentiala pe
ntru sisteme liniare analogice" }}{PARA 0 "" 0 "" {TEXT -1 35 "Sa cons
ideram ecuatia diferentiala:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
42 "Fy:=(D@@3)(y)(t)-3*(D@@2)(y)(t):Fx:=(D@@2)" }{TEXT -1 0 "" }
{MPLTEXT 1 0 27 "(e)(t)-e(t):eq:=\{Fy=Fx\}:eq;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<#/,&---%#@@G6$%\"DG\"\"$6#%\"yG6#%\"tG\"\"\"*&F,F1---F
)6$F+\"\"#F-F/F1!\"\",&--F56#%\"eGF/F1-F=F/F8" }}}{PARA 0 "" 0 "" 
{TEXT -1 89 "Consideram conditii initiale nule pentru iesire. Numarul \+
conditiilor initiale asupra lui " }{XPPEDIT 18 0 "y(t);" "6#-%\"yG6#%
\"tG" }{TEXT -1 36 " si a derivatelor sale este egal cu " }{XPPEDIT 
18 0 "n;" "6#%\"nG" }{TEXT -1 32 ", ordinul ecuatiei diferentiale." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "initcondy:=\{y(0)=0,D(y)(0)=
0,(D@@2)(y)(0)=0\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*initcondyG<%
/-%\"yG6#\"\"!F*/--%\"DG6#F(F)F*/---%#@@G6$F.\"\"#F/F)F*" }}}{PARA 0 "
" 0 "" {TEXT -1 65 "In general aceasta ecuatie diferentiala liniara se
 poate rezolva:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "dsolve(eq
 union initcondy,y(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%
\"tG-%$IntG6$-F)6$*&-F)6$*&-%$expG6#,$%\"uG!\"$\"\"\",&-%%diffG6$-%\"e
G6#F5-%\"$G6$F5\"\"#F7F<!\"\"F7/F5;\"\"!F'F7-F26#,$F'\"\"$F7F'F'" }}}
{PARA 0 "" 0 "" {TEXT -1 34 "Rezultatul este o expresie pentru " }
{XPPEDIT 18 0 "y(t);" "6#-%\"yG6#%\"tG" }{TEXT -1 90 " in care trebuie
 sa determinam 2 constante de integrare pe baza conditiilor initiale n
ule." }}{PARA 0 "" 0 "" {TEXT -1 57 "Putem considera conditii initiale
 nule si pentru intrare:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "
initcondx:=\{e(0)=0,D(e)(0)=0\}:" }}}{PARA 0 "" 0 "" {TEXT -1 79 "Apli
cind Transformata Laplace si luind in considerare conditiile initiale \+
nule:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "eqL:=subs(initcondy
,laplace(Fy,t,s))=subs(initcondx,laplace(Fx,t,s)):eqL;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/,&*&)%\"sG\"\"$\"\"\"-%\"YG6#F'F)F)*(F(F))F'\"\"#
F)F*F)!\"\",&*&F.F)-%\"EGF,F)F)F3F0" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "H:=(s)->solve(eqL,Y(s))/E(s):H:=H(s);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"HG*&,&*$)%\"sG\"\"#\"\"\"F+F+!\"\"F+*&F(F+,&F)
F+\"\"$F,F+F," }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 19 "Functia de tra
nsfer" }}{PARA 0 "" 0 "" {TEXT -1 78 "Interpretarea functiei de transf
er si reprezentarea ei pentru s numar complex:" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "H:=s/(s^2+0.1*s+100);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"HG*&%\"sG\"\"\",(*$)F&\"\"#F'F'*&$F'!\"\"F'F&F'F'\"
$+\"F'F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "PZ[numeric](H,s
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\")c.Pv-%'MATRIXG6#7
%7$%#z1G$\"\"!F.7$%#p1G^$$!%+]!\"&$\"%+5!\"#7$%#p2G^$F2$!%+5F7" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "PZ[grafic](H,s);" }}{PARA 
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&$\"%+5!\"#-%&COLORG6&%$RGBG\"\"\"\"\"!F2-%'SYMBOLG6$%&CROSSG\"#;-F$6%
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45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
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ntarea in spatiu a modulului f.d.t.\");" }}{PARA 13 "" 1 "" {GLPLOT3D 
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