{VERSION 4 0 "SGI MIPS UNIX" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 " " 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 767 "restart:\nprint(\"a cos wt + b sin wt\");\na:=2;\nb:=1;\nr:=evalf(sqrt(a^2+b^2));\nphase_ lag_degrees:=evalf(arctan(b,a)*180.0/Pi);\nomega:=1;\nwith(plottools): \nwith(plots):\nnframes:=50:\ndt:=2*Pi/nframes:\nfor i from 0 to nfram es do\n t:=i*dt:\n v1:=[a*cos(omega*t),a*sin(omega*t)];\n v2:=v1+[b *sin(omega*t),-b*cos(omega*t)];\n l1:=line([0,0],v1,color=red,thickne ss=2):\n l20:=line([0,0],[b*sin(omega*t),-b*cos(omega*t)],color=blue, thickness=2):\n l2:=line(v1,v2,color=blue,thickness=2):\n l2x:=line( [a*cos(omega*t),0],\n [a*cos(omega*t)+b*sin(omega*t),0],colo r=blue,thickness=2):\n l3:=line([0,0],v2,color=orange):\n c3:=circle ([0,0],r,color=orange):\n frame[i]:=display(l3,l20,l1,l2,c3):\nod:\nd isplay( seq(frame[i],i=0..nframes), insequence=true,scaling=constraine d );" }}{PARA 13 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q4a~cos~wt~+~b~sin~wt6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG \"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG$\"+yz1OA!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%2phase_lag_degreesG$\"+<^]cE!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&omegaG\"\"\"" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the nam e changecoords has been redefined\n" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%(ANIMATEG6U7'-%'CURVESG6$7$7$$\"\"!F-F,7$$\" \"#F-$!\"\"F--%'COLOURG6&%$RGBG$\")+++!)!\")$\")Vyg>F9F:-F(6%7$F+7$F,F 1-F46&F6F,F,$\"*++++\"F9-%*THICKNESSG6#F0-F(6%7$F+7$F/F,-F46&F6FBF,F,F D-F(6%7$FJF.F@FD-F(6$7U7$$\"+yz1OA!\"*F,7$$\"+9fV=AFV$\"+-j`-G!#57$$\" +\"zFV$\"+kRB x5FV7$$\"+&*p,4=FV$\"+\"yFVJ\"FV7$$\"+/M-I;FV$\"+jQpI:FV7$$\"+sLKD9FV$ \"+*)*>Hs\"FV7$$\"+Q^9)>\"FV$\"+PY(z)=FV7$$\"+,Wr?&*Ffn$\"+(zaK-#FV7$$ \"+X+$)4pFfn$\"+AqiE@FV7$$\"+kN(**=%Ffn$\"+n5Y'>#FV7$$\"+%pQSS\"Ffn$\" +4clJAFV7$$!+.(QSS\"FfnF\\r7$$!+tN(**=%Ffn$\"+m5Y'>#FV7$$!+a+$)4pFfn$ \"+@qiE@FV7$$!+!R92_*Ffn$\"+)zaK-#FV7$$!+P^9)>\"FV$\"+QY(z)=FV7$$!+rLK D9FV$\"+!**>Hs\"FV7$$!+2M-I;FV$\"+hQpI:FV7$$!+'*p,4=FV$\"+zxK98FV7$$!+ 28[f>FV$\"+iRBx5FV7$$!+FM/z?FV$\"+C_^J#)Ffn7$$!+\"z7$Fdu$!+2j`-GFfn7$F _u$!+M\\(3c&Ffn7$Fjt$!+U_^J#)Ffn7$$!+18[f>FV$!+kRBx5FV7$$!+&*p,4=FV$!+ !yFVJ\"FV7$$!+0M-I;FV$!+iQpI:FV7$$!+qLKD9FV$!+\"**>Hs\"FV7$$!+O^9)>\"F V$!+RY(z)=FV7$$!+uVr?&*Ffn$!+*zaK-#FV7$$!+O+$)4pFfn$!+AqiE@FV7$$!+bN(* *=%Ffn$!+n5Y'>#FV7$$!+&oQSS\"Ffn$!+4clJAFV7$$\"+8(QSS\"FfnFby7$$\"+\"e t**=%Ffn$!+m5Y'>#FV7$$\"+j+$)4pFfn$!+@qiE@FV7$$\"+*R92_*Ffn$!+(zaK-#FV 7$Ffp$!+PY(z)=FV7$Fap$!+*)*>Hs\"FV7$$\"+2M-I;FV$!+gQpI:FV7$$\"+(*p,4=F V$!+yxK98FV7$$\"+38[f>FV$!+hRBx5FV7$$\"+GM/z?FV$!+:_^J#)Ffn7$Fhn$!+3\\ (3c&Ffn7$FX$!+!GOD!GFfn7$FT$\"+2/]M=!#=F37'-F(6$7$F+7$$\"+PEc4@FV$!+TB [9uFfnF3-F(6%7$F+7$$\"+OBL`7Ffn$!+8q9@**FfnF@FD-F(6%7$F+7$$\"+.%HU)>FV $\"+sYm1DFfnFKFD-F(6%7$F^^lF^]lF@FDFP7'-F(6$7$F+7$$\"+4i&e=#FV$!+nQ.7Z FfnF3-F(6%7$F+7$$\"+s))*o[#Ffn$!+6;$eo*FfnF@FD-F(6%7$F+7$$\"+Aj;P>FV$ \"+Wxzt\\FfnFKFD-F(6%7$Fj_lFj^lF@FDFP7'-F(6$7$F+7$$\"+DvnFAFV$!+0QFN>F fnF3-F(6%7$F+7$$\"+FbC\"o$Ffn$!+f[w(H*FfnF@FD-F(6%7$F+7$$\"+sHbf=FV$\" +a5\\itFfnFKFD-F(6%7$FfalFf`lF@FDFP7'-F(6$7$F+7$$\"+MqOMAFV$\"*#o1?()F fnF3-F(6%7$F+7$$\"+Tn`<[Ffn$!++o1j()FfnF@FD-F(6%7$F+7$$\"+gLh_e?#FV$\"+2^`lOFfn F3-F(6%7$F+7$$\"+CD&y(eFfn$!+V*p,4)FfnF@FD-F(6%7$F+7$$\"+*)R.=;FV$\"+0 0dv6FVFKFD-F(6%7$F^elF^dlF@FDFP7'-F(6$7$F+7$$\"+hV[U@FV$\"+ZeD,kFfnF3- F(6%7$F+7$$\"+g5ZXoFfn$!+tio*G(FfnF@FD-F(6%7$F+7$$\"+bs$zX\"FV$\"+7U4p 8FVFKFD-F(6%7$FjflFjelF@FDFP7'-F(6$7$F+7$$\"+A7OX?FV$\"+j\\-O!*FfnF3-F (6%7$F+7$$\"+GC80xFfn$!+(*)RUP'FfnF@FD-F(6%7$F+7$$\"+zz%[F\"FV$\"+'[E5 a\"FVFKFD-F(6%7$FfhlFfglF@FDFP7'-F(6$7$F+7$$\"+::)f\">FV$\"+c!HG:\"FVF 3-F(6%7$F+7$$\"+a#zKW)Ffn$!+^zEe`FfnF@FD-F(6%7$F+7$$\"+!f`;2\"FV$\"+^e l)o\"FVFKFD-F(6%7$FbjlFbilF@FDFP7'-F(6$7$F+7$$\"+OcQcxFVFKFD-F(6%7$Ff_mFf^mF@FDFP7'-F(6$7$F+7$$\"+nxgB6FV$\"+QHEL>FV F3-F(6%7$F+7$$\"+%Gn-)**Ffn$!+D>0zi!#6F@FD-F(6%7$F+7$$\"+&Q5eD\"Ffn$\" +dM0'*>FVFKFD-F(6%7$FcamFb`mF@FDFP7'-F(6$7$F+7$$\"+**oXC()Ffn$\"+wR%)e ?FVF3-F(6%7$F+7$F[am$\"+D>0ziF_amF@FD-F(6%7$F+7$$!+&Q5eD\"FfnFfamFKFD- F(6%7$F]cmF_bmF@FDFP7'-F(6$7$F+7$$\"+CiCvgFfn$\"+;e&>:#FVF3-F(6%7$F+7$ F__m$\"+UJ\"Q(=FfnF@FD-F(6%7$F+7$$!+%GEwu$FfnFi_mFKFD-F(6%7$FedmFgcmF@ FDFP7'-F(6$7$F+7$$\"+*GD-L$Ffn$\"+F+86AFVF3-F(6%7$F+7$Fc]m$\"+Q*p,4$Ff nF@FD-F(6%7$F+7$$!+w)R.='FfnF]^mFKFD-F(6%7$F]fmF_emF@FDFP7'-F(6$7$F+7$ $\"*(o%oK&Ffn$\"+(RLaB#FVF3-F(6%7$F+7$Fg[m$\"+=HzdUFfnF@FD-F(6%7$F+7$$ !+Oee:&)FfnFa\\mFKFD-F(6%7$FegmFgfmF@FDFP7'-F(6$7$F+7$$!+YmDtAFfn$\"+Y E[CAFVF3-F(6%7$F+7$F[jl$\"+^zEe`FfnF@FD-F(6%7$F+7$$!+!f`;2\"FVFejlFKFD -F(6%7$F]imF_hmF@FDFP7'-F(6$7$F+7$$!+itMV]Ffn$\"+w/Xy@FVF3-F(6%7$F+7$F _hl$\"+(*)RUP'FfnF@FD-F(6%7$F+7$$!+zz%[F\"FVFihlFKFD-F(6%7$FejmFgimF@F DFP7'-F(6$7$F+7$$!+!\\,Rt(Ffn$\"+RG1)4#FVF3-F(6%7$F+7$Fcfl$\"+tio*G(Ff nF@FD-F(6%7$F+7$$!+bs$zX\"FVF]glFKFD-F(6%7$F]\\nF_[nF@FDFP7'-F(6$7$F+7 $$!+P([-.\"FV$\"+*\\(e%)>FVF3-F(6%7$F+7$Fgdl$\"+V*p,4)FfnF@FD-F(6%7$F+ 7$$!+*)R.=;FVFaelFKFD-F(6%7$Fe]nFg\\nF@FDFP7'-F(6$7$F+7$$!+'of3F\"FV$ \"+GS\")R=FVF3-F(6%7$F+7$F[cl$\"++o1j()FfnF@FD-F(6%7$F+7$$!+gLh_%G9\\\"FV$\"+\"fDgm\"FVF3-F (6%7$F+7$F_al$\"+f[w(H*FfnF@FD-F(6%7$F+7$$!+sHbf=FVFialFKFD-F(6%7$Fe`n Fg_nF@FDFP7'-F(6$7$F+7$$!+NkZ)o\"FV$\"+OH'fY\"FVF3-F(6%7$F+7$Fc_l$\"+6 ;$eo*FfnF@FD-F(6%7$F+7$$!+Aj;P>FVF]`lFKFD-F(6%7$F]bnF_anF@FDFP7'-F(6$7 $F+7$$!+ph*)e=FV$\"+o6yU7FVF3-F(6%7$F+7$Fg]l$\"+8q9@**FfnF@FD-F(6%7$F+ 7$$!+.%HU)>FVFa^lFKFD-F(6%7$FecnFgbnF@FDFP7'-F(6$7$F+7$$!\"#F-$\"\"\"F -F3-F(6%7$F+7$F,FbdnF@FD-F(6%7$F+7$F`dnF,FKFD-F(6%7$F[enF_dnF@FDFP7'-F (6$7$F+7$$!+PEc4@FV$\"+TB[9uFfnF3-F(6%7$F+7$$!+OBL`7FfnF`cnF@FD-F(6%7$ F+7$Ffcn$!+sYm1DFfnFKFD-F(6%7$FafnFcenF@FDFP7'-F(6$7$F+7$$!+4i&e=#FV$ \"+nQ.7ZFfnF3-F(6%7$F+7$$!+s))*o[#FfnFhanF@FD-F(6%7$F+7$F^bn$!+Wxzt\\F fnFKFD-F(6%7$FignF[gnF@FDFP7'-F(6$7$F+7$$!+DvnFAFV$\"+0QFN>FfnF3-F(6%7 $F+7$$!+FbC\"o$FfnF``nF@FD-F(6%7$F+7$Ff`n$!+a5\\itFfnFKFD-F(6%7$FainFc hnF@FDFP7'-F(6$7$F+7$$!+MqOMAFV$!*#o1?()FfnF3-F(6%7$F+7$$!+Tn`<[FfnFh^ nF@FD-F(6%7$F+7$F^_n$!+#[t]j*FfnFKFD-F(6%7$FijnF[jnF@FDFP7'-F(6$7$F+7$ $!+T#>e?#FV$!+2^`lOFfnF3-F(6%7$F+7$$!+CD&y(eFfnF`]nF@FD-F(6%7$F+7$Ff]n $!+00dv6FVFKFD-F(6%7$Fa\\oFc[oF@FDFP7'-F(6$7$F+7$$!+hV[U@FV$!+ZeD,kFfn F3-F(6%7$F+7$$!+g5ZXoFfnFh[nF@FD-F(6%7$F+7$F^\\n$!+7U4p8FVFKFD-F(6%7$F i]oF[]oF@FDFP7'-F(6$7$F+7$$!+A7OX?FV$!+j\\-O!*FfnF3-F(6%7$F+7$$!+GC80x FfnF`jmF@FD-F(6%7$F+7$Ffjm$!+'[E5a\"FVFKFD-F(6%7$Fa_oFc^oF@FDFP7'-F(6$ 7$F+7$$!+::)f\">FV$!+c!HG:\"FVF3-F(6%7$F+7$$!+a#zKW)FfnFhhmF@FD-F(6%7$ F+7$F^im$!+^el)o\"FVFKFD-F(6%7$Fi`oF[`oF@FDFP7'-F(6$7$F+7$$!+OcQcFVFKFD-F(6%7$FicoF[coF@FDF P7'-F(6$7$F+7$$!+z)\\qN\"FV$!+)=$>xFVFKFD-F(6%7$FaeoFcdoF@FDFP7'-F(6$7$F+7$$!+nx gB6FV$!+QHEL>FVF3-F(6%7$F+7$$!+%Gn-)**FfnFhbmF@FD-F(6%7$F+7$F^cm$!+dM0 '*>FVFKFD-F(6%7$FifoF[foF@FDFP7'-F(6$7$F+7$$!+**oXC()Ffn$!+wR%)e?FVF3- F(6%7$F+7$FdfoF]amF@FD-F(6%7$F+7$FdamFjfoFKFD-F(6%7$F_hoFcgoF@FDFP7'-F (6$7$F+7$$!+CiCvgFfn$!+;e&>:#FVF3-F(6%7$F+7$F\\eoFa_mF@FD-F(6%7$F+7$Fg _mFbeoFKFD-F(6%7$FcioFghoF@FDFP7'-F(6$7$F+7$$!+*GD-L$Ffn$!+F+86AFVF3-F (6%7$F+7$FdcoFe]mF@FD-F(6%7$F+7$F[^mFjcoFKFD-F(6%7$FgjoF[joF@FDFP7'-F( 6$7$F+7$$!*(o%oK&Ffn$!+(RLaB#FVF3-F(6%7$F+7$F\\boFi[mF@FD-F(6%7$F+7$F_ \\mFbboFKFD-F(6%7$F[\\pF_[pF@FDFP7'-F(6$7$F+7$$\"+YmDtAFfn$!+YE[CAFVF3 -F(6%7$F+7$Fd`oF]jlF@FD-F(6%7$F+7$FcjlFj`oFKFD-F(6%7$F_]pFc\\pF@FDFP7' -F(6$7$F+7$$\"+itMV]Ffn$!+w/Xy@FVF3-F(6%7$F+7$F\\_oFahlF@FD-F(6%7$F+7$ FghlFb_oFKFD-F(6%7$Fc^pFg]pF@FDFP7'-F(6$7$F+7$$\"+!\\,Rt(Ffn$!+RG1)4#F VF3-F(6%7$F+7$Fd]oFeflF@FD-F(6%7$F+7$F[glFj]oFKFD-F(6%7$Fg_pF[_pF@FDFP 7'-F(6$7$F+7$$\"+P([-.\"FV$!+*\\(e%)>FVF3-F(6%7$F+7$F\\\\oFidlF@FD-F(6 %7$F+7$F_elFb\\oFKFD-F(6%7$F[apF_`pF@FDFP7'-F(6$7$F+7$$\"+'of3F\"FV$!+ GS\")R=FVF3-F(6%7$F+7$FdjnF]clF@FD-F(6%7$F+7$FcclFjjnFKFD-F(6%7$F_bpFc apF@FDFP7'-F(6$7$F+7$$\"+>%G9\\\"FV$!+\"fDgm\"FVF3-F(6%7$F+7$F\\inFaal F@FD-F(6%7$F+7$FgalFbinFKFD-F(6%7$FccpFgbpF@FDFP7'-F(6$7$F+7$$\"+NkZ)o \"FV$!+OH'fY\"FVF3-F(6%7$F+7$FdgnFe_lF@FD-F(6%7$F+7$F[`lFjgnFKFD-F(6%7 $FgdpF[dpF@FDFP7'-F(6$7$F+7$$\"+ph*)e=FV$!+o6yU7FVF3-F(6%7$F+7$F\\fnFi ]lF@FD-F(6%7$F+7$F_^lFbfnFKFD-F(6%7$F[fpF_epF@FDFPF&-%(SCALINGG6#%,CON STRAINEDG" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Cu rve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" }}}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 7 "?arctan" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 9 0" 2 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }