(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 185618, 4782]*) (*NotebookOutlinePosition[ 186333, 4807]*) (* CellTagsIndexPosition[ 186289, 4803]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ \(DSolve[h\ \(c'\)[t] \[Equal] F0\ *\ \((1 + Sin[f\ t])\)\ - \ u\ c[t], c[t], t]\)], "Input"], Cell[BoxData[ \({{c[ t] \[Rule] \[ExponentialE]\^\(-\(\(t\ u\)\/h\)\)\ C[ 1] + \((F0\ \((f\^2\ h\^2 + u\^2 - f\ h\ u\ Cos[f\ t] + f\^2\ h\^2\ Sin[f\ t] + 2\ u\^2\ Sin[f\ t] - f\ h\ u\ Cos[f\ t]\ Sin[f\ t] + u\^2\ Sin[f\ t]\^2)\))\)/\((\((f\ h - \[ImaginaryI]\ u)\ \)\ \((f\ h + \[ImaginaryI]\ u)\)\ u\ \((Cos[\(f\ t\)\/2] + Sin[\(f\ t\)\/2])\ \)\^2)\)}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(solution = Simplify\ [\((F0\ \((f\^2\ h\^2 + u\^2 - f\ h\ u\ Cos[f\ t] + f\^2\ h\^2\ Sin[f\ t] + 2\ u\^2\ Sin[f\ t] - f\ h\ u\ Cos[f\ t]\ Sin[f\ t] + u\^2\ Sin[f\ t]\^2)\))\)/\((\((f\ h - \[ImaginaryI]\ u)\)\ \ \((f\ h + \[ImaginaryI]\ u)\)\ u\ \((Cos[\(f\ t\)\/2] + Sin[\(f\ \ t\)\/2])\)\^2)\)]\)], "Input"], Cell[BoxData[ \(\(F0\ \((f\^2\ h\^2 + u\^2 - f\ h\ u\ Cos[f\ t] + u\^2\ Sin[f\ \ t])\)\)\/\(f\^2\ h\^2\ u + u\^3\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s1 = solution /. {F0 \[Rule] 1, f \[Rule] 0, u \[Rule] 2, h \[Rule] 10}\)], "Input"], Cell[BoxData[ \(1\/2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p1 = Plot[s1, {t, 0, 20}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.047619 0.0147151 0.588604 [ [.2619 .00222 -3 -9 ] [.2619 .00222 3 0 ] [.5 .00222 -6 -9 ] [.5 .00222 6 0 ] [.7381 .00222 -6 -9 ] [.7381 .00222 6 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.01131 .13244 -18 -4.5 ] [.01131 .13244 0 4.5 ] [.01131 .25016 -18 -4.5 ] [.01131 .25016 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .4856 -18 -4.5 ] [.01131 .4856 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .2619 .01472 m .2619 .02097 L s [(5)] .2619 .00222 0 1 Mshowa .5 .01472 m .5 .02097 L s [(10)] .5 .00222 0 1 Mshowa .7381 .01472 m .7381 .02097 L s [(15)] .7381 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(20)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .21429 .01472 m .21429 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .40476 .01472 m .40476 .01847 L s .45238 .01472 m .45238 .01847 L s .54762 .01472 m .54762 .01847 L s .59524 .01472 m .59524 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .78571 .01472 m .78571 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .13244 m .03006 .13244 L s [(0.2)] .01131 .13244 1 0 Mshowa .02381 .25016 m .03006 .25016 L s [(0.4)] .01131 .25016 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(0.6)] .01131 .36788 1 0 Mshowa .02381 .4856 m .03006 .4856 L s [(0.8)] .01131 .4856 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .16187 m .02756 .16187 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .27959 m .02756 .27959 L s .02381 .30902 m .02756 .30902 L s .02381 .33845 m .02756 .33845 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .45617 m .02756 .45617 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .30902 m .06244 .30902 L .10458 .30902 L .14415 .30902 L .18221 .30902 L .22272 .30902 L .26171 .30902 L .30316 .30902 L .34309 .30902 L .3815 .30902 L .42237 .30902 L .46172 .30902 L .49955 .30902 L .53984 .30902 L .57861 .30902 L .61984 .30902 L .65954 .30902 L .69774 .30902 L .73838 .30902 L .77751 .30902 L .81909 .30902 L .85916 .30902 L .89771 .30902 L .93871 .30902 L .97619 .30902 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgWoo00D007ooOomo o`00009oo`03001oogoo005oo`00EGoo00<007ooOol0>goo00D007ooOomoo`00009oo`03001oogoo 03Moo`03001oogoo009oo`03001oogoo03Moo`04001oogoo0002Ool01000Oomoo`000goo001EOol3 000jOol20004Ool2000iOol20004Ool3000hOol20004Ool20004Ool00?moob5oo`005Goo00<007oo Ool0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007oo Ool0ogoo2Goo000?Oooo000A0001Ool001Eoo`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo 00Yoo`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo 00Yoo`03001oogoo00Yoo`03001oogoo00Uoo`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo 00Yoo`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo 00Yoo`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo00Eoo`005Goo00<007ooOol0?Woo00<0 07ooOol0?Goo00<007ooOol0?Woo00<007ooOol0?Woo00<007ooOol01Goo000EOol00`00Oomoo`3o Ool9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3o Ool9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo0P00ogoo2Woo000EOol00`00Oomoo`3oOol9Ool0 01Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool0 01Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool0 01Eoo`800?moo`Yoo`005Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03 001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03 001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo000EOol2003oOol:Ool001Eoo`03001oogoo 0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo 0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo0002Ool20004Ool20003Ool40004Ool00`00Oomoo`3o Ool9Ool00005Ool007ooOol00008Ool00`00Oomoo`05Ool00`00Oomoo`3oOol9Ool00005Ool007oo Ool00009Ool00`00Oomoo`04Ool3003oOol9Ool00005Ool007ooOol0000:Ool00`00Oomoo`03Ool0 0`00Oomoo`3oOol9Ool00005Ool007ooOol00008Ool01000Oomoo`0017oo00<007ooOol0ogoo2Goo 0002Ool2000:Ool20005Ool00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<0 07ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo0P00 ogoo2Woo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0 ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0 ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`800?moo`Yoo`005Goo00<007ooOol0ogoo2Goo 000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo 000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo 000EOol2003oOol:Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo000EOol0 0`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo0002Ool2 0004Ool20005Ool30003Ool00`00Oomoo`3oOol9Ool00005Ool007ooOol0000;Ool00`00Oomoo`02 Ool00`00Oomoo`3oOol9Ool00005Ool007ooOol00008Ool50003Ool3003oOol9Ool00005Ool007oo Ool00008Ool01000Oomoo`0017oo00<007ooOol0ogoo2Goo00001Goo001oogoo00002Goo00<007oo 000017oo00<007ooOol0ogoo2Goo0002Ool2000;Ool20004Ool00`00Oomoo`3oOol9Ool001Eoo`03 001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03 001oogoo0?moo`Uoo`005Goo0P00ogoo2Woo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo 0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo 0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoool000D000Mo o`005Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uo o`005Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uo o`005Goo00<007ooOol0ogoo2Goo000EOol2003oOol:Ool001Eoo`03001oogoo0?moo`Uoo`005Goo 00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo 00<007ooOol0ogoo2Goo0002Ool20004Ool20003Ool30005Ool00`00Oomoo`3oOol9Ool00005Ool0 07ooOol00008Ool01000Oomoo`0017oo00<007ooOol0ogoo2Goo00001Goo001oogoo000027oo00@0 07ooOol000Aoo`<00?moo`Uoo`0000Eoo`00Oomoo`0000Qoo`<000Eoo`03001oogoo0?moo`Uoo`00 00Eoo`00Oomoo`0000Uoo`03001oogoo00Aoo`03001oogoo0?moo`Uoo`000Woo0P002Woo0`0017oo 00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo 00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`800?moo`Yoo`005Goo00<007oo Ool0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007oo Ool0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007oo Ool0ogoo2Goo000EOol2003oOol:Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo 2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo 2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo0P00ogoo2Woo000E Ool00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo000E Ool00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`000Woo0P0017oo0P0017oo0P001Goo 00<007ooOol0ogoo2Goo00001Goo001oogoo000027oo00@007ooOol000Aoo`03001oogoo0?moo`Uo o`0000Eoo`00Oomoo`0000Qoo`04001oogoo0004Ool3003oOol9Ool00005Ool007ooOol00009Ool2 0005Ool00`00Oomoo`3oOol9Ool00005Ool007ooOol00008Ool01000Oomoo`0017oo00<007ooOol0 ogoo2Goo0002Ool2000:Ool20005Ool00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`00 5Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`00 5Goo0P00ogoo2Woo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<0 07ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<0 07ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`800?moo`Yoo`005Goo00<007ooOol0 ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0 ogoo2Goo000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0 ogoo2Goo000EOol2003oOol:Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo 000EOol00`00Oomoo`3oOol9Ool001Eoo`03001oogoo0?moo`Uoo`005Goo00<007ooOol0ogoo2Goo 000=Ool50003Ool00`00Oomoo`3oOol9Ool000moo`03001oogoo00=oo`03001oogoo0?moo`Uoo`00 3goo00<007ooOol00goo0`00ogoo2Goo000?Ool00`00Oomoo`03Ool00`00Oomoo`3oOol9Ool000mo o`03001oogoo00=oo`03001oogoo0?moo`Uoo`003Woo0P001Goo00<007ooOol0ogoo2Goo000EOol0 0`00Oomoo`3oOol9Ool00001\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-1.65971, -0.07747, \ 0.0772359, 0.00624851}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s2 = solution /. {F0 \[Rule] 1, f \[Rule] 0.5, u \[Rule] 2, h \[Rule] 10}\)], "Input"], Cell[BoxData[ \(0.017241379310344827`\ \((\(\(29.`\)\(\[InvisibleSpace]\)\) - 10.`\ Cos[0.5`\ t] + 4\ Sin[0.5`\ t])\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p2 = Plot[s2, {t, 0, 20}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.047619 -0.483416 1.58487 [ [.2619 .13803 -3 -9 ] [.2619 .13803 3 0 ] [.5 .13803 -6 -9 ] [.5 .13803 6 0 ] [.7381 .13803 -6 -9 ] [.7381 .13803 6 0 ] [.97619 .13803 -6 -9 ] [.97619 .13803 6 0 ] [.01131 .07129 -24 -4.5 ] [.01131 .07129 0 4.5 ] [.01131 .22977 -24 -4.5 ] [.01131 .22977 0 4.5 ] [.01131 .30902 -18 -4.5 ] [.01131 .30902 0 4.5 ] [.01131 .38826 -24 -4.5 ] [.01131 .38826 0 4.5 ] [.01131 .4675 -18 -4.5 ] [.01131 .4675 0 4.5 ] [.01131 .54675 -24 -4.5 ] [.01131 .54675 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .2619 .15053 m .2619 .15678 L s [(5)] .2619 .13803 0 1 Mshowa .5 .15053 m .5 .15678 L s [(10)] .5 .13803 0 1 Mshowa .7381 .15053 m .7381 .15678 L s [(15)] .7381 .13803 0 1 Mshowa .97619 .15053 m .97619 .15678 L s [(20)] .97619 .13803 0 1 Mshowa .125 Mabswid .07143 .15053 m .07143 .15428 L s .11905 .15053 m .11905 .15428 L s .16667 .15053 m .16667 .15428 L s .21429 .15053 m .21429 .15428 L s .30952 .15053 m .30952 .15428 L s .35714 .15053 m .35714 .15428 L s .40476 .15053 m .40476 .15428 L s .45238 .15053 m .45238 .15428 L s .54762 .15053 m .54762 .15428 L s .59524 .15053 m .59524 .15428 L s .64286 .15053 m .64286 .15428 L s .69048 .15053 m .69048 .15428 L s .78571 .15053 m .78571 .15428 L s .83333 .15053 m .83333 .15428 L s .88095 .15053 m .88095 .15428 L s .92857 .15053 m .92857 .15428 L s .25 Mabswid 0 .15053 m 1 .15053 L s .02381 .07129 m .03006 .07129 L s [(0.35)] .01131 .07129 1 0 Mshowa .02381 .22977 m .03006 .22977 L s [(0.45)] .01131 .22977 1 0 Mshowa .02381 .30902 m .03006 .30902 L s [(0.5)] .01131 .30902 1 0 Mshowa .02381 .38826 m .03006 .38826 L s [(0.55)] .01131 .38826 1 0 Mshowa .02381 .4675 m .03006 .4675 L s [(0.6)] .01131 .4675 1 0 Mshowa .02381 .54675 m .03006 .54675 L s [(0.65)] .01131 .54675 1 0 Mshowa .125 Mabswid .02381 .08714 m .02756 .08714 L s .02381 .10298 m .02756 .10298 L s .02381 .11883 m .02756 .11883 L s .02381 .13468 m .02756 .13468 L s .02381 .16638 m .02756 .16638 L s .02381 .18223 m .02756 .18223 L s .02381 .19808 m .02756 .19808 L s .02381 .21392 m .02756 .21392 L s .02381 .24562 m .02756 .24562 L s .02381 .26147 m .02756 .26147 L s .02381 .27732 m .02756 .27732 L s .02381 .29317 m .02756 .29317 L s .02381 .32487 m .02756 .32487 L s .02381 .34071 m .02756 .34071 L s .02381 .35656 m .02756 .35656 L s .02381 .37241 m .02756 .37241 L s .02381 .40411 m .02756 .40411 L s .02381 .41996 m .02756 .41996 L s .02381 .43581 m .02756 .43581 L s .02381 .45165 m .02756 .45165 L s .02381 .48335 m .02756 .48335 L s .02381 .4992 m .02756 .4992 L s .02381 .51505 m .02756 .51505 L s .02381 .5309 m .02756 .5309 L s .02381 .05544 m .02756 .05544 L s .02381 .03959 m .02756 .03959 L s .02381 .02374 m .02756 .02374 L s .02381 .00789 m .02756 .00789 L s .02381 .5626 m .02756 .5626 L s .02381 .57844 m .02756 .57844 L s .02381 .59429 m .02756 .59429 L s .02381 .61014 m .02756 .61014 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .03576 m .04262 .06252 L .06244 .10108 L .10458 .21026 L .14264 .3259 L .18314 .44563 L .20184 .49386 L .22214 .53811 L .23322 .558 L .24344 .57339 L .25322 .58525 L .25863 .59057 L .26358 .59464 L .26808 .59767 L .27299 .60025 L .27569 .60133 L .27818 .60212 L .28057 .6027 L .28191 .60294 L .28312 .6031 L .28426 .60322 L .28548 .60329 L .28651 .60332 L .28764 .60331 L .28887 .60325 L .29018 .60313 L .29141 .60297 L .29254 .60278 L .29472 .60229 L .2971 .60159 L .30142 .59984 L .30627 .59717 L .31082 .59399 L .32119 .5843 L .3313 .57173 L .3422 .55486 L .38334 .46455 L .42296 .3503 L .46107 .23353 L .50163 .12276 L .52037 .08181 L .54068 .04737 L .55179 .03347 L .55666 .02854 L .56203 .02397 L .56674 .02069 L .57181 .01796 L .57461 .0168 L .57717 .01597 L .5784 .01564 L Mistroke .57974 .01534 L .58092 .01513 L .58218 .01495 L .58281 .01488 L .58351 .01481 L .58474 .01474 L .58543 .01472 L .58617 .01472 L .58687 .01473 L .58751 .01475 L .58874 .01484 L .58944 .01491 L .59008 .01499 L .59134 .01518 L .59252 .01541 L .59468 .01595 L .59707 .01671 L .60189 .01882 L .60716 .02197 L .61199 .02563 L .62287 .03654 L .6327 .04944 L .64184 .06391 L .66255 .10484 L .70165 .2064 L .7432 .33257 L .78323 .45023 L .80159 .49707 L .82175 .54045 L .84167 .57315 L .85255 .58623 L .86272 .59518 L .86772 .59839 L .87035 .59977 L .87316 .60098 L .8756 .60183 L .87689 .60221 L .87829 .60255 L .87957 .60281 L .88075 .603 L .88187 .60314 L .88305 .60325 L .88421 .6033 L .88527 .60332 L .88648 .60329 L .88763 .60322 L .8887 .60312 L .88968 .60299 L .8919 .60258 L .89414 .60201 L Mistroke .89661 .6012 L .9016 .59895 L .9068 .59576 L .91174 .59194 L .92102 .58271 L .93101 .56988 L .94191 .55262 L .97619 .47883 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg7oo00D007oo Oomoo`00009oo`03001oogoo005oo`006goo00<007ooOol02Goo00<007ooOol0;goo00<007ooOol0 >Woo00D007ooOomoo`00009oo`03001oogoo02Moo`03001oogoo00aoo`03001oogoo009oo`03001o ogoo03Eoo`04001oogoo0002Ool01000Oomoo`000goo000KOol00`00Oomoo`0:Ool00`00Oomoo`0^ Ool3000iOol20002Ool01000Ool00000:Woo00<007ooOol02goo0P0017oo0`00=Woo0P0017oo0P00 17oo000KOol00`00Oomoo`0:Ool00`00Oomoo`1^Ool00`00Oomoo`0/Ool00`00Oomoo`1EOol001]o o`8000]oo`03001oogoo06ioo`03001oogoo02aoo`03001oogoo05Eoo`006goo00<007ooOol02goo 00<007ooOol0K7oo00<007ooOol0;Goo00<007ooOol0EGoo000KOol00`00Oomoo`0;Ool00`00Oomo o`1/Ool00`00Oomoo`0^Ool00`00Oomoo`1DOol001]oo`03001oogoo00aoo`03001oogoo06Yoo`03 001oogoo02moo`03001oogoo05Aoo`0057ooo`003@00000KOol00`00Oomoo`09Ool01000Oomoo`00 2Goo00<007ooOol02Woo00<007ooOol02Goo00<007ooOol02Woo00<007ooOol02Woo00<007ooOol0 2Goo00<007ooOol02Woo00<007ooOol02Woo00<007ooOol01goo00<007oo000037oo00<007ooOol0 2Woo00<007ooOol02Goo00<007ooOol027oo00<007oo000037oo00<007ooOol02Goo00<007ooOol0 2Woo00<007ooOol02Woo00<007ooOol02Goo00<007ooOol02Woo00<007ooOol01Goo000KOol00`00 Oomoo`0=Ool00`00Oomoo`0/Ool00`00Oomoo`0iOol01000Oomoo`00<7oo00<007ooOol037oo00<0 07ooOol0?7oo00<007ooOol01Goo000KOol00`00Oomoo`0=Ool00`00Oomoo`1XOol00`00Oomoo`0b Ool00`00Oomoo`1BOol001]oo`8000ioo`03001oogoo06Qoo`03001oogoo039oo`03001oogoo059o o`006goo00<007ooOol03Woo00<007ooOol0IWoo00<007ooOol0Ool00`00Oomoo`1VOol00`00Oomoo`0dOol00`00Oomoo`1AOol001]oo`03001oogoo 00moo`03001oogoo06Eoo`03001oogoo03Aoo`03001oogoo055oo`006goo0P0047oo00<007ooOol0 I7oo00<007ooOol0=Goo00<007ooOol0DGoo000KOol00`00Oomoo`0?Ool00`00Oomoo`1TOol00`00 Oomoo`0fOol00`00Oomoo`1@Ool001]oo`03001oogoo011oo`03001oogoo069oo`03001oogoo03Mo o`03001oogoo051oo`006goo00<007ooOol047oo00<007ooOol0HWoo00<007ooOol0>7oo00<007oo Ool0Cgoo000KOol00`00Oomoo`0@Ool00`00Oomoo`1ROol00`00Oomoo`0hOol00`00Oomoo`1?Ool0 01]oo`80019oo`03001oogoo061oo`03001oogoo03Uoo`03001oogoo04moo`006goo00<007ooOol0 4Goo00<007ooOol0H7oo00<007ooOol0>Woo00<007ooOol0CWoo000KOol00`00Oomoo`0BOol00`00 Oomoo`1OOol00`00Oomoo`0jOol00`00Oomoo`1>Ool001]oo`03001oogoo019oo`03001oogoo05io o`03001oogoo03]oo`03001oogoo04ioo`006goo0P004goo00<007ooOol0GWoo00<007ooOol0?7oo 00<007ooOol0CGoo000KOol00`00Oomoo`0COol00`00Oomoo`1LOol00`00Oomoo`0mOol00`00Oomo o`1=Ool0009oo`8000Aoo`8000Eoo`<0009oo`8000Eoo`03001oogoo01=oo`03001oogoo05aoo`03 001oogoo03eoo`03001oogoo04eoo`0000Eoo`00Oomoo`0000]oo`04001oogoo0002Ool00`00Oomo o`02Ool00`00Oomoo`0COol00`00Oomoo`1LOol00`00Oomoo`0nOol00`00Oomoo`1Ool00`00Oomoo`1Ool00`00Oomoo`1Ool00`00Oomoo`14Ool000Qoo`8000Yoo`<000Aoo`03001oogoo01]oo`03001oogoo04ao o`03001oogoo04ioo`03001oogoo04Aoo`006goo0P007Goo00<007ooOol0BWoo00<007ooOol0Cgoo 00<007ooOol0A7oo000KOol00`00Oomoo`0LOol00`00Oomoo`1:Ool00`00Oomoo`1@Ool00`00Oomo o`13Ool001]oo`03001oogoo01aoo`03001oogoo04Yoo`03001oogoo051oo`03001oogoo04=oo`00 6goo00<007ooOol07Goo00<007ooOol0B7oo00<007ooOol0DGoo00<007ooOol0@goo000KOol2000N Ool00`00Oomoo`18Ool00`00Oomoo`1BOol00`00Oomoo`12Ool001]oo`03001oogoo01eoo`03001o ogoo04Qoo`03001oogoo059oo`03001oogoo049oo`006goo00<007ooOol07Woo00<007ooOol0AWoo 00<007ooOol0Dgoo00<007ooOol0@Woo000KOol00`00Oomoo`0NOol00`00Oomoo`16Ool00`00Oomo o`1DOol00`00Oomoo`11Ool001]oo`03001oogoo01ioo`03001oogoo04Ioo`03001oogoo05Aoo`03 001oogoo045oo`006goo0P0087oo00<007ooOol0A7oo00<007ooOol0EGoo00<007ooOol0@Goo000K Ool00`00Oomoo`0OOol00`00Oomoo`14Ool00`00Oomoo`1FOol00`00Oomoo`10Ool001]oo`03001o ogoo021oo`03001oogoo04=oo`03001oogoo05Ioo`03001oogoo041oo`006goo00<007ooOol087oo 00<007ooOol0@Woo00<007ooOol0Egoo00<007ooOol0@7oo000KOol2000QOol00`00Oomoo`12Ool0 0`00Oomoo`1HOol00`00Oomoo`0oOol001]oo`03001oogoo025oo`03001oogoo041oo`03001oogoo 05Uoo`03001oogoo03moo`000Woo0P0017oo0P0017oo0P0017oo0P001Goo00<007ooOol08Goo00<0 07ooOol0@7oo00<007ooOol0FGoo00<007ooOol0?goo00001Goo001oogoo000027oo00@007ooOol0 009oo`04001oogoo0004Ool00`00Oomoo`0QOol00`00Oomoo`10Ool00`00Oomoo`1JOol00`00Oomo o`0nOol00005Ool007ooOol0000;Ool00`00Oomoo`03Ool00`00Oomoo`02Ool2000SOol00`00Oomo o`0nOol00`00Oomoo`1KOol00`00Oomoo`0nOol00005Ool007ooOol00009Ool20004Ool20005Ool0 0`00Oomoo`0ROol00`00Oomoo`0nOol00`00Oomoo`1KOol00`00Oomoo`0nOol00005Ool007ooOol0 0009Ool00`00Oomoo`03Ool00`00Oomoo`04Ool00`00Oomoo`0ROol00`00Oomoo`0nOol00`00Oomo o`1LOol00`00Oomoo`0mOol0009oo`8000Yoo`<000=oo`<000Aoo`03001oogoo02=oo`03001oogoo 03aoo`03001oogoo05eoo`03001oogoo03eoo`006goo0P0097oo00<007ooOol0?7oo00<007ooOol0 GWoo00<007ooOol0?7oo000KOol00`00Oomoo`0SOol00`00Oomoo`0lOol00`00Oomoo`1NOol00`00 Oomoo`0lOol001]oo`03001oogoo02Aoo`03001oogoo03Yoo`03001oogoo05moo`03001oogoo03ao o`006goo00<007ooOol097oo00<007ooOol0>Woo00<007ooOol0H7oo00<007ooOol0>goo000KOol0 0`00Oomoo`0UOol00`00Oomoo`0hOol00`00Oomoo`1QOol00`00Oomoo`0kOol001]oo`8002Ioo`03 001oogoo03Qoo`03001oogoo065oo`03001oogoo03]oo`006goo00<007ooOol09Goo00<007ooOol0 >7oo00<007ooOol0HWoo00<007ooOol0>Woo000KOol00`00Oomoo`0VOol00`00Oomoo`0fOol00`00 Oomoo`1SOol00`00Oomoo`0jOol001]oo`03001oogoo02Ioo`03001oogoo03Ioo`03001oogoo06=o o`03001oogoo03Yoo`006goo0P009goo00<007ooOol0=Woo00<007ooOol0I7oo00<007ooOol0>Goo 000KOol00`00Oomoo`0WOol00`00Oomoo`0dOol00`00Oomoo`1UOol00`00Oomoo`0iOol001]oo`03 001oogoo02Moo`03001oogoo03Aoo`03001oogoo06Eoo`03001oogoo03Uoo`006goo00<007ooOol0 9goo00<007ooOol07oo000KOol2000YOol00`00Oomoo`0b Ool00`00Oomoo`1WOol00`00Oomoo`0hOol001]oo`03001oogoo02Qoo`03001oogoo039oo`03001o ogoo06Moo`03001oogoo03Qoo`0027oo0P0017oo0P000goo0`001Goo00<007ooOol0:Goo00<007oo Ool0<7oo00<007ooOol0JGoo00<007ooOol0=goo0007Ool01000Oomoo`0027oo00@007ooOol000Ao o`03001oogoo02Uoo`03001oogoo031oo`03001oogoo06Uoo`03001oogoo03Moo`001goo00@007oo Ool000Qoo`04001oogoo0004Ool2000ZOol00`00Oomoo`0`Ool00`00Oomoo`1ZOol00`00Oomoo`0f Ool000Moo`04001oogoo0008Ool30005Ool00`00Oomoo`0ZOol00`00Oomoo`0^Ool00`00Oomoo`1[ Ool00`00Oomoo`0fOol000Moo`04001oogoo0009Ool00`00Oomoo`04Ool00`00Oomoo`0ZOol00`00 Oomoo`0^Ool00`00Oomoo`1[Ool00`00Oomoo`0fOol000Qoo`8000Yoo`<000Aoo`03001oogoo02Yo o`03001oogoo02eoo`03001oogoo06eoo`03001oogoo02eoo`03001oogoo00Eoo`006goo0P00;7oo 00<007ooOol0;7oo00<007ooOol0KGoo00<007ooOol0;Goo00<007ooOol01Goo000KOol00`00Oomo o`0[Ool00`00Oomoo`0/Ool00`00Oomoo`1^Ool00`00Oomoo`0[Ool00`00Oomoo`06Ool001]oo`03 001oogoo02aoo`03001oogoo02Yoo`03001oogoo06moo`03001oogoo02]oo`03001oogoo00Ioo`00 6goo00<007ooOol0;7oo00<007ooOol0:Woo00<007ooOol0L7oo00<007ooOol0:Goo00<007ooOol0 1goo000KOol00`00Oomoo`0/Ool00`00Oomoo`0YOol00`00Oomoo`1aOol00`00Oomoo`0YOol00`00 Oomoo`07Ool001]oo`8002ioo`03001oogoo02Qoo`03001oogoo075oo`03001oogoo02Qoo`03001o ogoo00Qoo`006goo00<007ooOol0;Goo00<007ooOol09goo00<007ooOol0Lgoo00<007ooOol09goo 00<007ooOol027oo000KOol00`00Oomoo`0^Ool00`00Oomoo`0VOol00`00Oomoo`1cOol00`00Oomo o`0VOol00`00Oomoo`09Ool001]oo`03001oogoo02ioo`03001oogoo02Ioo`03001oogoo07Aoo`03 001oogoo02Eoo`03001oogoo00Uoo`006goo0P00<7oo00<007ooOol097oo00<007ooOol0MGoo00<0 07ooOol09Goo00<007ooOol02Goo000KOol00`00Oomoo`0_Ool00`00Oomoo`0TOol00`00Oomoo`1e Ool00`00Oomoo`0TOol00`00Oomoo`0:Ool001]oo`03001oogoo031oo`03001oogoo029oo`03001o ogoo07Moo`03001oogoo02=oo`03001oogoo00Yoo`006goo00<007ooOol0<7oo00<007ooOol08Woo 00<007ooOol0Mgoo00<007ooOol08Woo00<007ooOol02goo000KOol2000bOol00`00Oomoo`0QOol0 0`00Oomoo`1hOol00`00Oomoo`0QOol00`00Oomoo`0;Ool001]oo`03001oogoo035oo`03001oogoo 021oo`03001oogoo07Uoo`03001oogoo021oo`03001oogoo00aoo`000Woo0P0017oo0P000goo0`00 17oo0P001Goo00<007ooOol07oo00<007ooOol04goo00<007ooOol0QWoo 00<007ooOol04goo00<007ooOol04Woo000KOol2000iOol00`00Oomoo`0BOol00`00Oomoo`27Ool0 0`00Oomoo`0BOol00`00Oomoo`0COol001]oo`03001oogoo03Uoo`03001oogoo011oo`03001oogoo 08Uoo`03001oogoo011oo`03001oogoo01Aoo`006goo00<007ooOol0>Woo00<007ooOol03Woo00<0 07ooOol0Rgoo00<007ooOol03Woo00<007ooOol05Goo000KOol00`00Oomoo`0kOol2000=Ool00`00 Oomoo`2=Ool2000=Ool00`00Oomoo`0FOol001]oo`8003ioo`03001oogoo00Uoo`03001oogoo091o o`03001oogoo00Qoo`8001Uoo`006goo00<007ooOol0?Woo0P001goo0P00U7oo0P001goo00<007oo Ool06Goo000KOol00`00Oomoo`10Ool7002HOol7000LOol001]oo`03001oogoo0?moo`=oo`006goo 0P00ogoo17oo000KOol00`00Oomoo`3oOol3Ool001]oo`03001oogoo0?moo`=oo`00ogoo8Goo003o OolQOol00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-2.15729, 0.290149, \ 0.0789457, 0.002372}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s3 = solution /. {F0 \[Rule] 1, f \[Rule] 1, u \[Rule] 2, h \[Rule] 10}\)], "Input"], Cell[BoxData[ \(1\/208\ \((104 - 20\ Cos[t] + 4\ Sin[t])\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p3 = Plot[s3, {t, 0, 20}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.047619 -1.19164 3.00131 [ [.2619 -0.00361 -3 -9 ] [.2619 -0.00361 3 0 ] [.5 -0.00361 -6 -9 ] [.5 -0.00361 6 0 ] [.7381 -0.00361 -6 -9 ] [.7381 -0.00361 6 0 ] [.97619 -0.00361 -6 -9 ] [.97619 -0.00361 6 0 ] [.01131 .15895 -24 -4.5 ] [.01131 .15895 0 4.5 ] [.01131 .30902 -18 -4.5 ] [.01131 .30902 0 4.5 ] [.01131 .45908 -24 -4.5 ] [.01131 .45908 0 4.5 ] [.01131 .60915 -18 -4.5 ] [.01131 .60915 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .2619 .00889 m .2619 .01514 L s [(5)] .2619 -0.00361 0 1 Mshowa .5 .00889 m .5 .01514 L s [(10)] .5 -0.00361 0 1 Mshowa .7381 .00889 m .7381 .01514 L s [(15)] .7381 -0.00361 0 1 Mshowa .97619 .00889 m .97619 .01514 L s [(20)] .97619 -0.00361 0 1 Mshowa .125 Mabswid .07143 .00889 m .07143 .01264 L s .11905 .00889 m .11905 .01264 L s .16667 .00889 m .16667 .01264 L s .21429 .00889 m .21429 .01264 L s .30952 .00889 m .30952 .01264 L s .35714 .00889 m .35714 .01264 L s .40476 .00889 m .40476 .01264 L s .45238 .00889 m .45238 .01264 L s .54762 .00889 m .54762 .01264 L s .59524 .00889 m .59524 .01264 L s .64286 .00889 m .64286 .01264 L s .69048 .00889 m .69048 .01264 L s .78571 .00889 m .78571 .01264 L s .83333 .00889 m .83333 .01264 L s .88095 .00889 m .88095 .01264 L s .92857 .00889 m .92857 .01264 L s .25 Mabswid 0 .00889 m 1 .00889 L s .02381 .15895 m .03006 .15895 L s [(0.45)] .01131 .15895 1 0 Mshowa .02381 .30902 m .03006 .30902 L s [(0.5)] .01131 .30902 1 0 Mshowa .02381 .45908 m .03006 .45908 L s [(0.55)] .01131 .45908 1 0 Mshowa .02381 .60915 m .03006 .60915 L s [(0.6)] .01131 .60915 1 0 Mshowa .125 Mabswid .02381 .0389 m .02756 .0389 L s .02381 .06891 m .02756 .06891 L s .02381 .09893 m .02756 .09893 L s .02381 .12894 m .02756 .12894 L s .02381 .18896 m .02756 .18896 L s .02381 .21898 m .02756 .21898 L s .02381 .24899 m .02756 .24899 L s .02381 .279 m .02756 .279 L s .02381 .33903 m .02756 .33903 L s .02381 .36904 m .02756 .36904 L s .02381 .39906 m .02756 .39906 L s .02381 .42907 m .02756 .42907 L s .02381 .4891 m .02756 .4891 L s .02381 .51911 m .02756 .51911 L s .02381 .54912 m .02756 .54912 L s .02381 .57913 m .02756 .57913 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .02043 m .02846 .02743 L .03279 .03636 L .04262 .06486 L .0522 .10261 L .06244 .15217 L .10458 .40237 L .12445 .50749 L .13567 .55272 L .14102 .56967 L .14603 .58258 L .15047 .5915 L .15275 .59514 L .15525 .59835 L .15666 .59982 L .15797 .60095 L .15932 .6019 L .16055 .60254 L .16176 .60299 L .1629 .60324 L .16411 .60332 L .16541 .60319 L .16669 .60285 L .16789 .60234 L .1692 .60157 L .17061 .6005 L .17349 .59751 L .17611 .59387 L .18117 .58443 L .18596 .57261 L .19561 .54087 L .20586 .49677 L .22428 .3974 L .26204 .1711 L .27146 .12267 L .28138 .07958 L .28658 .06087 L .29226 .04379 L .29743 .03154 L .30224 .02307 L .30487 .01966 L .30729 .0173 L .30855 .01637 L .30995 .01558 L .31065 .01528 L .3114 .01503 L .31211 .01486 L .31276 .01476 L .31403 .01473 L .3152 .01488 L Mistroke .31649 .01525 L .31721 .01555 L .31786 .01589 L .31906 .01664 L .32035 .01766 L .3227 .02006 L .32494 .02301 L .32741 .02699 L .33238 .03729 L .34128 .06303 L .35152 .10314 L .36083 .14795 L .38176 .26806 L .4025 .39482 L .42166 .49821 L .43127 .53956 L .44028 .56986 L .44481 .58162 L .44968 .59152 L .45232 .59565 L .45509 .59905 L .45745 .60117 L .45879 .60206 L .46004 .60267 L .46132 .60309 L .46197 .60322 L .46268 .6033 L .46393 .60329 L .46511 .60309 L .46582 .60288 L .46649 .60262 L .46775 .60198 L .46911 .60106 L .47059 .59979 L .47309 .597 L .47575 .59316 L .48054 .58405 L .48509 .57278 L .48937 .56 L .49914 .52345 L .51929 .42172 L .53779 .31036 L .55829 .1874 L .56829 .13422 L .57738 .09246 L .58685 .05738 L .59119 .04454 L .59579 .03332 L .59812 .0286 L .60069 .02419 L Mistroke .60306 .02086 L .60522 .01844 L .60644 .01734 L .60777 .01636 L .6085 .01592 L .60917 .01557 L .60986 .01528 L .61051 .01506 L .61177 .01479 L .61291 .01472 L .61413 .01483 L .61482 .01498 L .61546 .01517 L .61672 .01571 L .61792 .01641 L .62016 .01822 L .62258 .02089 L .62521 .02463 L .62993 .03353 L .6343 .04418 L .64432 .07685 L .65497 .12272 L .69274 .34066 L .71373 .46247 L .72292 .50778 L .73296 .54882 L .73769 .56454 L .74273 .57856 L .7475 .58901 L .75182 .59608 L .75437 .59914 L .75672 .60122 L .75795 .60203 L .7593 .60269 L .75998 .60294 L .76071 .60313 L .76203 .60331 L .76327 .60327 L .76397 .60316 L .76462 .603 L .76581 .60257 L .76707 .60191 L .76831 .60106 L .76948 .60008 L .77167 .59777 L .77634 .59081 L .78147 .58006 L .78682 .5655 L .7918 .54901 L .81029 .46665 L Mistroke .84927 .23525 L .86914 .12614 L .88035 .07739 L .8857 .05851 L .89071 .04368 L .89552 .03218 L .89992 .02414 L .90243 .02065 L .90481 .01807 L .90603 .01703 L .90733 .01613 L .90808 .01572 L .90876 .0154 L .90939 .01516 L .91008 .01496 L .91136 .01474 L .91207 .01472 L .91272 .01475 L .9139 .01495 L .91516 .01536 L .91587 .01568 L .91663 .0161 L .91803 .01707 L .92066 .01955 L .92317 .02276 L .92583 .02703 L .93062 .03692 L .93999 .06407 L .95008 .10389 L .96836 .19784 L .97619 .24394 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg7oo00D007ooOomo o`00009oo`03001oogoo005oo`00FGoo00<007ooOol0>Woo00D007ooOomoo`00009oo`03001oogoo 03Ioo`03001oogoo009oo`03001oogoo03Eoo`04001oogoo0002Ool01000Oomoo`000goo001IOol3 000iOol20004Ool2000hOol20004Ool3000fOol20004Ool20004Ool00?moob5oo`00ogoo8Goo003o OolQOol001]oo`03001oogoo0?moo`=oo`006goo00<007ooOol0ogoo0goo000DOooo000=000001]o o`03001oogoo00Uoo`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo00Uoo`03001oogoo00Yo o`03001oogoo00Yoo`03001oogoo00Uoo`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo00Uo o`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo00Uoo`03001oogoo00Yoo`03001oogoo00Yo o`03001oogoo00Uoo`03001oogoo00Yoo`03001oogoo00Yoo`03001oogoo00Uoo`03001oogoo00Yo o`03001oogoo00Eoo`006goo00<007ooOol0?7oo00<007ooOol02Goo1@00;Woo00<007ooOol06Woo 10007goo00<007ooOol0:Woo10003Woo00<007ooOol01Goo000KOol00`00Oomoo`18Ool01@00Oomo ogoo0000BWoo00@007ooOomoo`8004Yoo`05001oogooOol0000FOol001]oo`03001oogoo04Moo`03 001oogoo00=oo`03001oogoo04Ioo`03001oogoo00Aoo`03001oogoo04Ioo`03001oogoo00=oo`03 001oogoo01=oo`006goo0P00B7oo00<007ooOol017oo00<007ooOol0AGoo00<007ooOol017oo00<0 07ooOol0AWoo00<007ooOol017oo00<007ooOol04Woo000KOol20017Ool00`00Oomoo`05Ool00`00 Oomoo`15Ool00`00Oomoo`05Ool00`00Oomoo`14Ool00`00Oomoo`05Ool00`00Oomoo`0BOol001]o o`03001oo`0004Eoo`03001oogoo00Moo`03001oogoo04=oo`03001oogoo00Ioo`03001oogoo04=o o`03001oogoo00Moo`03001oogoo015oo`006goo0`00AGoo00<007ooOol01goo00<007ooOol0@goo 00<007ooOol01Woo00<007ooOol0@goo00<007ooOol01goo00<007ooOol04Goo000KOol01000Oomo o`00@goo00<007ooOol027oo00<007ooOol0@Woo00<007ooOol027oo00<007ooOol0@Goo00<007oo Ool027oo00<007ooOol04Goo000KOol01000Oomoo`00@goo00<007ooOol02Goo00<007ooOol0@Goo 00<007ooOol027oo00<007ooOol0@Goo00<007ooOol02Goo00<007ooOol047oo000KOol01000Oomo o`00@goo00<007ooOol02Goo00<007ooOol0@Goo00<007ooOol02Goo00<007ooOol0@7oo00<007oo Ool02Goo00<007ooOol047oo000KOol01@00Oomoogoo0000@Goo00<007ooOol02Woo00<007ooOol0 @7oo00<007ooOol02Woo00<007ooOol0?goo00<007ooOol02goo00<007ooOol03goo000KOol01@00 Oomoogoo0000@Goo00<007ooOol02Woo00<007ooOol0@7oo00<007ooOol02Woo00<007ooOol0?goo 00<007ooOol02goo00<007ooOol03goo000KOol00`00Oomoo`02Ool00`00Oomoo`0nOol00`00Oomo o`0;Ool00`00Oomoo`0oOol00`00Oomoo`0;Ool00`00Oomoo`0nOol00`00Oomoo`0Ool001]oo`03001oogoo009oo`03001oogoo03ioo`03001oogoo00]oo`03001oogoo03ioo`03 001oogoo00aoo`03001oogoo03ioo`03001oogoo00aoo`03001oogoo00ioo`006goo0P000goo00<0 07ooOol0?Goo00<007ooOol037oo00<007ooOol0?Woo00<007ooOol037oo00<007ooOol0?Goo00<0 07ooOol03Goo00<007ooOol03Woo000KOol00`00Oomoo`02Ool00`00Oomoo`0mOol00`00Oomoo`0= Ool00`00Oomoo`0mOol00`00Oomoo`0=Ool00`00Oomoo`0lOol00`00Oomoo`0=Ool00`00Oomoo`0> Ool001]oo`03001oogoo00=oo`03001oogoo03]oo`03001oogoo00ioo`03001oogoo03aoo`03001o ogoo00ioo`03001oogoo03aoo`03001oogoo00ioo`03001oogoo00eoo`006goo00<007ooOol00goo 00<007ooOol0>goo00<007ooOol03Woo00<007ooOol0?7oo00<007ooOol03Woo00<007ooOol0?7oo 00<007ooOol03Woo00<007ooOol03Goo000KOol00`00Oomoo`03Ool00`00Oomoo`0kOol00`00Oomo o`0>Ool00`00Oomoo`0lOol00`00Oomoo`0>Ool00`00Oomoo`0lOol00`00Oomoo`0>Ool00`00Oomo o`0=Ool001]oo`03001oogoo00=oo`03001oogoo03]oo`03001oogoo00moo`03001oogoo03Yoo`03 001oogoo011oo`03001oogoo03Yoo`03001oogoo00moo`03001oogoo00eoo`006goo00<007ooOol0 0goo00<007ooOol0>Woo00<007ooOol047oo00<007ooOol0>Woo00<007ooOol047oo00<007ooOol0 >Woo00<007ooOol03goo00<007ooOol03Goo000KOol00`00Oomoo`04Ool00`00Oomoo`0iOol00`00 Oomoo`0@Ool00`00Oomoo`0jOol00`00Oomoo`0@Ool00`00Oomoo`0jOol00`00Oomoo`0@Ool00`00 Oomoo`0Goo00<007ooOol04Goo00<007ooOol0>7oo00<007ooOol04Woo00<007ooOol0>7oo 00<007ooOol04Goo00<007ooOol037oo000KOol00`00Oomoo`04Ool00`00Oomoo`0iOol00`00Oomo o`0AOol00`00Oomoo`0hOol00`00Oomoo`0BOol00`00Oomoo`0hOol00`00Oomoo`0AOol00`00Oomo o`07oo00<007ooOol04Woo00<007ooOol0 >7oo00<007ooOol04Woo00<007ooOol02goo000KOol00`00Oomoo`05Ool00`00Oomoo`0gOol00`00 Oomoo`0COol00`00Oomoo`0gOol00`00Oomoo`0COol00`00Oomoo`0fOol00`00Oomoo`0COol00`00 Oomoo`0;Ool001]oo`03001oogoo00Eoo`03001oogoo03Moo`03001oogoo01=oo`03001oogoo03Mo o`03001oogoo01=oo`03001oogoo03Ioo`03001oogoo01=oo`03001oogoo00]oo`006goo00<007oo Ool01Goo00<007ooOol0=goo00<007ooOol04goo00<007ooOol0=Woo00<007ooOol057oo00<007oo Ool0=Woo00<007ooOol04goo00<007ooOol02goo000KOol20007Ool00`00Oomoo`0fOol00`00Oomo o`0COol00`00Oomoo`0fOol00`00Oomoo`0DOol00`00Oomoo`0fOol00`00Oomoo`0COol00`00Oomo o`0;Ool001]oo`03001oogoo00Ioo`03001oogoo03Eoo`03001oogoo01Aoo`03001oogoo03Ioo`03 001oogoo01Eoo`03001oogoo03Eoo`03001oogoo01Aoo`03001oogoo00Yoo`006goo00<007ooOol0 1Woo00<007ooOol0=Goo00<007ooOol057oo00<007ooOol0=Woo00<007ooOol05Goo00<007ooOol0 =7oo00<007ooOol05Goo00<007ooOol02Woo000KOol00`00Oomoo`06Ool00`00Oomoo`0eOol00`00 Oomoo`0EOol00`00Oomoo`0eOol00`00Oomoo`0EOol00`00Oomoo`0dOol00`00Oomoo`0EOol00`00 Oomoo`0:Ool001]oo`03001oogoo00Moo`03001oogoo03Aoo`03001oogoo01Eoo`03001oogoo03Ao o`03001oogoo01Ioo`03001oogoo03Aoo`03001oogoo01Eoo`03001oogoo00Yoo`006goo00<007oo Ool01goo00<007ooOol0 Ool00`00Oomoo`0UOol00`00Oomoo`0UOol00`00Oomoo`0UOol00`00Oomoo`0TOol00`00Oomoo`0U Ool00`00Oomoo`0ZOol000Moo`04001oogoo000;Ool00`00Oomoo`02Ool2000?Ool00`00Oomoo`0U Ool00`00Oomoo`0UOol00`00Oomoo`0UOol00`00Oomoo`0UOol00`00Oomoo`0TOol00`00Oomoo`0Z Ool000Moo`04001oogoo0009Ool20005Ool00`00Oomoo`0>Ool00`00Oomoo`0UOol00`00Oomoo`0U Ool00`00Oomoo`0UOol00`00Oomoo`0UOol00`00Oomoo`0TOol00`00Oomoo`0ZOol000Moo`04001o ogoo0009Ool00`00Oomoo`04Ool00`00Oomoo`0>Ool00`00Oomoo`0UOol00`00Oomoo`0UOol00`00 Oomoo`0UOol00`00Oomoo`0UOol00`00Oomoo`0SOol00`00Oomoo`0[Ool000Qoo`8000Yoo`<000Ao o`03001oogoo00ioo`03001oogoo02Aoo`03001oogoo02Ioo`03001oogoo02Eoo`03001oogoo02Eo o`03001oogoo02=oo`03001oogoo02]oo`006goo00<007ooOol03goo00<007ooOol08goo00<007oo Ool09goo00<007ooOol08goo00<007ooOol09Woo00<007ooOol08goo00<007ooOol0:goo000KOol0 0`00Oomoo`0?Ool00`00Oomoo`0SOol00`00Oomoo`0WOol00`00Oomoo`0SOol00`00Oomoo`0VOol0 0`00Oomoo`0SOol00`00Oomoo`0[Ool001]oo`03001oogoo00moo`03001oogoo02=oo`03001oogoo 02Moo`03001oogoo02=oo`03001oogoo02Moo`03001oogoo029oo`03001oogoo02]oo`006goo00<0 07ooOol03goo00<007ooOol08goo00<007ooOol09goo00<007ooOol08goo00<007ooOol09goo00<0 07ooOol08Woo00<007ooOol0:goo000KOol2000@Ool00`00Oomoo`0SOol00`00Oomoo`0WOol00`00 Oomoo`0SOol00`00Oomoo`0WOol00`00Oomoo`0QOol00`00Oomoo`0/Ool001]oo`03001oogoo00mo o`03001oogoo029oo`03001oogoo02Uoo`03001oogoo029oo`03001oogoo02Moo`03001oogoo025o o`03001oogoo02aoo`006goo00<007ooOol047oo00<007ooOol08Goo00<007ooOol0:Goo00<007oo Ool08Goo00<007ooOol0:7oo00<007ooOol08Goo00<007ooOol0;7oo000KOol00`00Oomoo`0@Ool0 0`00Oomoo`0QOol00`00Oomoo`0YOol00`00Oomoo`0QOol00`00Oomoo`0XOol00`00Oomoo`0QOol0 0`00Oomoo`0/Ool001]oo`03001oogoo011oo`03001oogoo025oo`03001oogoo02Uoo`03001oogoo 025oo`03001oogoo02Uoo`03001oogoo021oo`03001oogoo02aoo`006goo00<007ooOol047oo00<0 07ooOol08Goo00<007ooOol0:Goo00<007ooOol08Goo00<007ooOol0:Goo00<007ooOol087oo00<0 07ooOol0;7oo000KOol00`00Oomoo`0@Ool00`00Oomoo`0QOol00`00Oomoo`0YOol00`00Oomoo`0Q Ool00`00Oomoo`0YOol00`00Oomoo`0POol00`00Oomoo`0/Ool001]oo`03001oogoo011oo`03001o ogoo021oo`03001oogoo02]oo`03001oogoo021oo`03001oogoo02Uoo`03001oogoo01moo`03001o ogoo02eoo`006goo0P004Woo00<007ooOol07goo00<007ooOol0:goo00<007ooOol07goo00<007oo Ool0:Woo00<007ooOol07goo00<007ooOol0;Goo000KOol00`00Oomoo`0AOol00`00Oomoo`0OOol0 0`00Oomoo`0[Ool00`00Oomoo`0OOol00`00Oomoo`0ZOol00`00Oomoo`0OOol00`00Oomoo`0]Ool0 01]oo`03001oogoo015oo`03001oogoo01moo`03001oogoo02]oo`03001oogoo01moo`03001oogoo 02]oo`03001oogoo01ioo`03001oogoo02eoo`006goo00<007ooOol04Goo00<007ooOol07goo00<0 07ooOol0:goo00<007ooOol07goo00<007ooOol0:goo00<007ooOol07Woo00<007ooOol0;Goo000K Ool00`00Oomoo`0AOol00`00Oomoo`0OOol00`00Oomoo`0[Ool00`00Oomoo`0OOol00`00Oomoo`0[ Ool00`00Oomoo`0NOol00`00Oomoo`0]Ool001]oo`03001oogoo015oo`03001oogoo01ioo`03001o ogoo02eoo`03001oogoo01ioo`03001oogoo02]oo`03001oogoo01eoo`03001oogoo02ioo`006goo 00<007ooOol04Woo00<007ooOol07Goo00<007ooOol0;Goo00<007ooOol07Goo00<007ooOol0;7oo 00<007ooOol07Goo00<007ooOol0;Woo000KOol00`00Oomoo`0BOol00`00Oomoo`0MOol00`00Oomo o`0]Ool00`00Oomoo`0MOol00`00Oomoo`0/Ool00`00Oomoo`0MOol00`00Oomoo`0^Ool001]oo`80 01=oo`03001oogoo01eoo`03001oogoo02eoo`03001oogoo01eoo`03001oogoo02aoo`03001oogoo 01eoo`03001oogoo02ioo`006goo00<007ooOol04Woo00<007ooOol07Goo00<007ooOol0;Goo00<0 07ooOol07Goo00<007ooOol0;Goo00<007ooOol077oo00<007ooOol0;Woo000KOol00`00Oomoo`0B Ool00`00Oomoo`0LOol00`00Oomoo`0_Ool00`00Oomoo`0LOol00`00Oomoo`0]Ool00`00Oomoo`0L Ool00`00Oomoo`0^Ool001]oo`03001oogoo019oo`03001oogoo01aoo`03001oogoo02moo`03001o ogoo01aoo`03001oogoo02eoo`03001oogoo01]oo`03001oogoo02moo`006goo00<007ooOol04goo 00<007ooOol06goo00<007ooOol0;goo00<007ooOol06goo00<007ooOol0;Woo00<007ooOol06goo 00<007ooOol0;goo000KOol00`00Oomoo`0COol00`00Oomoo`0KOol00`00Oomoo`0_Ool00`00Oomo o`0KOol00`00Oomoo`0^Ool00`00Oomoo`0KOol00`00Oomoo`0_Ool001]oo`03001oogoo01=oo`03 001oogoo01]oo`03001oogoo02moo`03001oogoo01]oo`03001oogoo02ioo`03001oogoo01]oo`03 001oogoo02moo`006goo00<007ooOol04goo00<007ooOol06goo00<007ooOol0;goo00<007ooOol0 6goo00<007ooOol0;Woo00<007ooOol06goo00<007ooOol0;goo000KOol2000DOol00`00Oomoo`0J Ool00`00Oomoo`0aOol00`00Oomoo`0JOol00`00Oomoo`0_Ool00`00Oomoo`0JOol00`00Oomoo`0_ Ool001]oo`03001oogoo01Aoo`03001oogoo01Uoo`03001oogoo035oo`03001oogoo01Uoo`03001o ogoo031oo`03001oogoo01Uoo`03001oogoo031oo`006goo00<007ooOol057oo00<007ooOol06Goo 00<007ooOol07oo00<007ooOol04Woo00<007ooOol0Goo00<007ooOol047oo00<007ooOol0>Goo00<007ooOol04Goo00<007ooOol0=7oo000K Ool2000JOol00`00Oomoo`0@Ool00`00Oomoo`0iOol00`00Oomoo`0@Ool00`00Oomoo`0jOol00`00 Oomoo`0@Ool00`00Oomoo`0dOol001]oo`03001oogoo01Uoo`03001oogoo011oo`03001oogoo03Uo o`03001oogoo011oo`03001oogoo03Yoo`03001oogoo011oo`03001oogoo03Aoo`006goo00<007oo Ool06Goo00<007ooOol047oo00<007ooOol0>Goo00<007ooOol047oo00<007ooOol0>Woo00<007oo Ool03goo00<007ooOol0=Goo000KOol00`00Oomoo`0IOol00`00Oomoo`0@Ool00`00Oomoo`0jOol0 0`00Oomoo`0?Ool00`00Oomoo`0jOol00`00Oomoo`0?Ool00`00Oomoo`0eOol001]oo`03001oogoo 01Yoo`03001oogoo00ioo`03001oogoo03]oo`03001oogoo00ioo`03001oogoo03]oo`03001oogoo 00moo`03001oogoo03Eoo`006goo00<007ooOol06Woo00<007ooOol03Woo00<007ooOol0>goo00<0 07ooOol03Woo00<007ooOol0>goo00<007ooOol03goo00<007ooOol0=Goo000KOol00`00Oomoo`0J Ool00`00Oomoo`0>Ool00`00Oomoo`0kOol00`00Oomoo`0>Ool00`00Oomoo`0lOol00`00Oomoo`0= Ool00`00Oomoo`0fOol001]oo`03001oogoo01Yoo`03001oogoo00ioo`03001oogoo03aoo`03001o ogoo00eoo`03001oogoo03aoo`03001oogoo00eoo`03001oogoo03Ioo`006goo0P0077oo00<007oo Ool037oo00<007ooOol0?Goo00<007ooOol03Goo00<007ooOol0?7oo00<007ooOol03Goo00<007oo Ool0=Woo000KOol00`00Oomoo`0KOol00`00Oomoo`07oo 000KOol00`00Oomoo`0LOol00`00Oomoo`09Ool00`00Oomoo`12Ool00`00Oomoo`07Ool00`00Oomo o`12Ool00`00Oomoo`08Ool00`00Oomoo`0hOol001]oo`8001ioo`03001oogoo00Moo`03001oogoo 04=oo`03001oogoo00Moo`03001oogoo049oo`03001oogoo00Moo`03001oogoo03Uoo`006goo00<0 07ooOol07Goo00<007ooOol01goo00<007ooOol0@goo00<007ooOol01Woo00<007ooOol0@goo00<0 07ooOol01goo00<007ooOol0>Goo000KOol00`00Oomoo`0NOol00`00Oomoo`05Ool00`00Oomoo`15 Ool00`00Oomoo`05Ool00`00Oomoo`14Ool00`00Oomoo`05Ool00`00Oomoo`0jOol001]oo`03001o ogoo01moo`03001oogoo00Aoo`03001oogoo04Eoo`03001oogoo00Aoo`03001oogoo04Eoo`03001o ogoo00Eoo`03001oogoo03Yoo`006goo00<007ooOol07goo00<007ooOol00goo00<007ooOol0Agoo 00<007ooOol00goo00<007ooOol0AWoo00<007ooOol017oo00<007ooOol0>Woo000KOol00`00Oomo o`0POol01000Oomoogoo0P00BWoo00D007ooOomoo`0004Yoo`04001oogooOol2000mOol000Qoo`80 00Aoo`8000=oo`<000Eoo`03001oogoo025oo`@004]oo`@004aoo`@003ioo`001goo00@007ooOol0 00Qoo`04001oogoo0004Ool00`00Oomoo`3oOol3Ool000Moo`04001oogoo0008Ool01000Oomoo`00 17oo0P00ogoo17oo0007Ool01000Oomoo`0027oo0`001Goo00<007ooOol0ogoo0goo0007Ool01000 Oomoo`002Goo00<007ooOol017oo00<007ooOol0ogoo0goo0008Ool2000:Ool3003oOol:Ool00?mo ob5oo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-2.15729, 0.384289, \ 0.0789457, 0.00125256}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s4 = solution /. {F0 \[Rule] 1, f \[Rule] 5, u \[Rule] 2, h \[Rule] 10}\)], "Input"], Cell[BoxData[ \(\(2504 - 100\ Cos[5\ t] + 4\ Sin[5\ t]\)\/5008\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p4 = Plot[s4, {t, 0, 20}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.047619 -7.05443 14.7269 [ [.2619 .29652 -3 -9 ] [.2619 .29652 3 0 ] [.5 .29652 -6 -9 ] [.5 .29652 6 0 ] [.7381 .29652 -6 -9 ] [.7381 .29652 6 0 ] [.97619 .29652 -6 -9 ] [.97619 .29652 6 0 ] [.01131 .01448 -24 -4.5 ] [.01131 .01448 0 4.5 ] [.01131 .16175 -24 -4.5 ] [.01131 .16175 0 4.5 ] [.01131 .45629 -24 -4.5 ] [.01131 .45629 0 4.5 ] [.01131 .60356 -24 -4.5 ] [.01131 .60356 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .2619 .30902 m .2619 .31527 L s [(5)] .2619 .29652 0 1 Mshowa .5 .30902 m .5 .31527 L s [(10)] .5 .29652 0 1 Mshowa .7381 .30902 m .7381 .31527 L s [(15)] .7381 .29652 0 1 Mshowa .97619 .30902 m .97619 .31527 L s [(20)] .97619 .29652 0 1 Mshowa .125 Mabswid .07143 .30902 m .07143 .31277 L s .11905 .30902 m .11905 .31277 L s .16667 .30902 m .16667 .31277 L s .21429 .30902 m .21429 .31277 L s .30952 .30902 m .30952 .31277 L s .35714 .30902 m .35714 .31277 L s .40476 .30902 m .40476 .31277 L s .45238 .30902 m .45238 .31277 L s .54762 .30902 m .54762 .31277 L s .59524 .30902 m .59524 .31277 L s .64286 .30902 m .64286 .31277 L s .69048 .30902 m .69048 .31277 L s .78571 .30902 m .78571 .31277 L s .83333 .30902 m .83333 .31277 L s .88095 .30902 m .88095 .31277 L s .92857 .30902 m .92857 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .02381 .01448 m .03006 .01448 L s [(0.48)] .01131 .01448 1 0 Mshowa .02381 .16175 m .03006 .16175 L s [(0.49)] .01131 .16175 1 0 Mshowa .02381 .45629 m .03006 .45629 L s [(0.51)] .01131 .45629 1 0 Mshowa .02381 .60356 m .03006 .60356 L s [(0.52)] .01131 .60356 1 0 Mshowa .125 Mabswid .02381 .04393 m .02756 .04393 L s .02381 .07339 m .02756 .07339 L s .02381 .10284 m .02756 .10284 L s .02381 .13229 m .02756 .13229 L s .02381 .1912 m .02756 .1912 L s .02381 .22066 m .02756 .22066 L s .02381 .25011 m .02756 .25011 L s .02381 .27956 m .02756 .27956 L s .02381 .33847 m .02756 .33847 L s .02381 .36793 m .02756 .36793 L s .02381 .39738 m .02756 .39738 L s .02381 .42683 m .02756 .42683 L s .02381 .48574 m .02756 .48574 L s .02381 .51519 m .02756 .51519 L s .02381 .54465 m .02756 .54465 L s .02381 .5741 m .02756 .5741 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01495 m .02499 .01864 L .02605 .02583 L .02729 .03857 L .02846 .05478 L .03053 .09285 L .03279 .14569 L .04262 .43544 L .0452 .50203 L .04762 .55169 L .04884 .57092 L .05015 .58684 L .05089 .59357 L .0516 .59836 L .05223 .6013 L .05293 .60303 L .05418 .6022 L .05532 .59707 L .05663 .58605 L .05786 .57088 L .06006 .53315 L .06244 .47899 L .07312 .16669 L .07571 .10265 L .07714 .07362 L .07849 .05099 L .07925 .04047 L .08009 .03099 L .08084 .02422 L .08154 .01954 L .0822 .01657 L .08292 .01491 L .08368 .01499 L .08439 .01675 L .08557 .02326 L .08686 .03538 L .08751 .04342 L .08821 .05338 L .08946 .07471 L .09411 .18556 L .09956 .34988 L .10195 .42105 L .10458 .49105 L .10582 .51952 L .10715 .54612 L .1083 .5654 L .10956 .58216 L .11029 .58977 L .11097 .59535 L .11162 .59932 L Mistroke .11231 .60206 L .11363 .60301 L .11482 .599 L .11552 .59455 L .11626 .58819 L .11757 .57269 L .11899 .55039 L .12054 .51984 L .12593 .37709 L .13096 .22333 L .13373 .14617 L .13635 .08567 L .13754 .06364 L .13879 .04441 L .13945 .03618 L .14017 .0286 L .14144 .0192 L .1426 .01514 L .14384 .01557 L .14501 .02054 L .14608 .0289 L .15603 .24645 L .16149 .41256 L .16417 .48504 L .16664 .53964 L .16785 .56093 L .16898 .57716 L .17016 .59008 L .17145 .59931 L .17277 .60321 L .17397 .60189 L .17463 .59917 L .17535 .59461 L .17666 .58215 L .17775 .56789 L .17895 .54823 L .18138 .49716 L .18575 .37744 L .19036 .23642 L .19522 .10646 L .19776 .05732 L .19846 .04685 L .1992 .03721 L .19984 .03021 L .20054 .02405 L .20186 .01664 L .2031 .01475 L .20431 .01773 L .20543 .02464 L .20649 .03485 L Mistroke .20764 .04964 L .2097 .08564 L .21216 .14191 L .2144 .20316 L .21939 .35472 L .22391 .48256 L .22637 .53747 L .2275 .55775 L .22869 .57539 L .22996 .58969 L .23113 .59842 L .23239 .60295 L .2331 .60323 L .23377 .602 L .23496 .59628 L .23608 .58675 L .23709 .5749 L .23818 .55865 L .24064 .51061 L .24291 .45422 L .24806 .30179 L .25076 .21971 L .25361 .14116 L .25611 .08416 L .25743 .06004 L .25884 .03959 L .26015 .02595 L .26133 .01815 L .26252 .01483 L .26364 .0159 L .26472 .02077 L .26591 .03038 L .26715 .04504 L .26831 .06279 L .27038 .10342 L .27261 .15778 L .28232 .44499 L .28497 .51133 L .28636 .54039 L .28785 .56583 L .28859 .57617 L .28928 .58443 L .29057 .59594 L .29178 .60193 L .29309 .60308 L .29428 .5993 L .29559 .58996 L .29625 .58324 L .29695 .5746 L .29822 .55539 L Mistroke .30069 .50597 L .30293 .44948 L .31222 .17372 L .31447 .11613 L .3169 .06629 L .3183 .04465 L .31957 .02976 L .32085 .01983 L .32207 .01523 L .32336 .01559 L .32409 .01816 L .32474 .02195 L .32602 .03324 L .32723 .04843 L .32864 .07146 L .32994 .09727 L .33287 .16912 L .33768 .31199 L .34285 .46339 L .34546 .5255 L .34675 .55036 L .34794 .56947 L .34901 .58328 L .35016 .5941 L .35131 .60083 L .35258 .60332 L .35375 .60097 L .35483 .59491 L .35602 .58403 L .35726 .568 L .35936 .53113 L .36166 .47852 L .36723 .31765 L .37249 .16212 L .37478 .10557 L .3772 .05853 L .37847 .04024 L .37914 .03246 L .37987 .02562 L .38114 .01759 L .38232 .01475 L .38363 .01689 L .38483 .02376 L .38553 .02981 L .38616 .03657 L .38757 .05602 L .39014 .10526 L .39256 .16514 L .40192 .44284 L .40448 .50747 L Mistroke .40587 .53704 L .40717 .56024 L .40837 .57756 L .40947 .58961 L .41069 .59864 L .41199 .60306 L .41267 .60319 L .41338 .60171 L .41467 .59491 L .41538 .58887 L .41605 .58178 L .41758 .56064 L .42013 .51136 L .42287 .44233 L .4279 .29188 L .43067 .20853 L .43327 .13751 L .43571 .08264 L .43699 .05947 L .43834 .03988 L .43948 .02758 L .44074 .01872 L .44188 .01502 L .44294 .01537 L .44425 .02079 L .44548 .03094 L .4466 .04405 L .44781 .06242 L .45052 .11744 L .45303 .18228 L .45833 .34175 L .46111 .42469 L .46405 .50134 L .46644 .55064 L .4678 .57203 L .46906 .58718 L .47022 .59682 L .47128 .60186 L .4725 .6032 L .47366 .60002 L .47475 .59307 L .47591 .58164 L .4769 .56867 L .47798 .55117 L .48041 .50121 L .48268 .4431 L .48773 .29225 L .4904 .21171 L .49324 .13435 L .49464 .10142 L Mistroke .49597 .07452 L .49726 .05267 L .49844 .03671 L .49957 .02542 L .50076 .01782 L .50196 .01477 L .50327 .01676 L .50392 .01981 L .50463 .02466 L .50592 .03747 L .50717 .05469 L .50833 .07455 L .51096 .13187 L .51375 .20733 L .51879 .36077 L .52126 .43334 L .52353 .49266 L .52555 .53705 L .52776 .57378 L .52892 .58736 L .52999 .59634 L .53112 .60187 L .53233 .60321 L .53359 .59957 L .5343 .59528 L .53495 .58992 L .53615 .57665 L .53743 .55797 L .53963 .51534 L .54205 .45588 L .54683 .31521 L .55203 .16139 L .55441 .10299 L .55572 .07619 L .55695 .05497 L .5581 .03892 L .55934 .02602 L .56047 .01845 L .5615 .01509 L .56282 .01583 L .56404 .02152 L .56474 .02694 L .56538 .03321 L .56682 .05177 L .5682 .07513 L .5697 .10604 L .57242 .17443 L .57757 .32833 L .5824 .46843 L .58473 .52355 L Mistroke .58694 .56418 L .58816 .58082 L .5888 .58783 L .58949 .5939 L .5907 .60097 L .59183 .60331 L .59253 .6027 L .59317 .60072 L .59388 .59701 L .59463 .59136 L .59589 .57794 L .59728 .5578 L .59983 .50722 L .60222 .44706 L .60739 .29301 L .61011 .21068 L .61301 .13208 L .61553 .07665 L .61697 .05213 L .61763 .04284 L .61832 .03441 L .61956 .02304 L .62069 .01681 L .62191 .01473 L .6226 .01568 L .62324 .01795 L .62451 .02632 L .62523 .03327 L .62589 .04106 L .62839 .08184 L .63066 .1325 L .63307 .197 L .63849 .36149 L .64115 .43911 L .64357 .50144 L .64561 .54429 L .64668 .56271 L .64783 .57878 L .64905 .59157 L .65018 .59933 L .65135 .60306 L .65241 .60262 L .65366 .59741 L .65481 .58822 L .65608 .57344 L .65741 .55278 L .65966 .50747 L .66212 .44522 L .66693 .30207 L .67216 .14964 L Mistroke .67455 .09312 L .67586 .06771 L .67709 .04802 L .67814 .0347 L .67926 .02405 L .68051 .01688 L .68166 .01472 L .68298 .01749 L .6842 .02509 L .68491 .03161 L .68555 .03885 L .68699 .05949 L .68988 .11747 L .6926 .18831 L .69735 .33145 L .69987 .40738 L .70258 .48114 L .70521 .53971 L .70645 .56158 L .70761 .578 L .70876 .59048 L .71002 .59935 L .71113 .60298 L .71231 .60247 L .71301 .60004 L .71365 .59643 L .71436 .59097 L .7151 .58354 L .71635 .56729 L .71772 .5444 L .72025 .4897 L .72261 .42721 L .73146 .16379 L .73389 .104 L .73521 .07665 L .73646 .05512 L .7376 .03909 L .73865 .02783 L .73982 .01933 L .74107 .01502 L .74172 .01479 L .7424 .01602 L .74364 .02208 L .7444 .02819 L .74511 .03558 L .74645 .05347 L .74891 .09915 L .75156 .1641 L .75639 .30655 L .76148 .45698 L Mistroke .76371 .51186 L .7661 .55839 L .76746 .57821 L .76871 .59145 L .76997 .59988 L .77116 .6032 L .77223 .60227 L .77337 .5972 L .77435 .58961 L .77542 .57782 L .77657 .56141 L .77781 .5396 L .78006 .49049 L .78508 .34938 L .79044 .18757 L .79304 .11973 L .7955 .06849 L .79657 .05097 L .7977 .03598 L .79895 .024 L .8001 .01725 L .80129 .01472 L .80257 .01716 L .80379 .02431 L .80489 .03489 L .80619 .05194 L .8076 .07592 L .81017 .13227 L .81585 .29492 L .82119 .4535 L .82361 .51329 L .82617 .5621 L .8275 .5806 L .82826 .58875 L .82896 .59476 L .83021 .6015 L .8309 .6031 L .83154 .6032 L .83274 .59983 L .83384 .59262 L .83506 .5803 L .83635 .56241 L .83851 .52213 L .8409 .46512 L .84624 .30857 L .84915 .22005 L .85186 .14502 L .85437 .08696 L .85665 .04749 L .85795 .03151 L Mistroke .85918 .0212 L .86048 .01552 L .86121 .01472 L .86189 .01551 L .86301 .02007 L .86421 .02939 L .86534 .04227 L .86638 .05733 L .86891 .10623 L .87131 .16582 L .88127 .45978 L .88378 .5205 L .88516 .54781 L .88646 .56892 L .88755 .58308 L .88874 .59427 L .89005 .60152 L .89126 .60328 L .89257 .59986 L .89379 .59173 L .89449 .58496 L .89513 .5775 L .89656 .55644 L .89943 .498 L .90214 .42702 L .90715 .27566 L .91184 .14132 L .9142 .08716 L .91541 .0644 L .91673 .0441 L .91748 .03485 L .91818 .02778 L .91884 .02243 L .91955 .01825 L .92024 .01571 L .9209 .01474 L .92212 .01666 L .92319 .0223 L .92437 .03264 L .92559 .04792 L .92674 .06609 L .93098 .16146 L .93558 .29631 L .94057 .44516 L .94298 .50619 L .9443 .53451 L .94554 .55716 L .94668 .57429 L .94773 .58666 L .94889 .59647 L Mistroke .95014 .60226 L .95123 .60319 L .95225 .60057 L .95336 .59389 L .95456 .58244 L .95581 .56579 L .95699 .546 L .9592 .49946 L .97619 .04948 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol2000>Ool2000>Ool2000>Ool2000>Ool2000=Ool00`00Ool0000=Ool00`00Ool0 000=Ool00`00Ool0000=Ool2000>Ool2000>Ool2000>Ool2000>Ool2000>Ool2000EOol0009oo`80 00]oo`8000=oo`8000Eoo`03001oogoo00aoo`8000ioo`8000ioo`8000ioo`8000ioo`8000ioo`80 00eoo`03001oo`0000eoo`03001oo`0000eoo`03001oo`0000eoo`03001oo`0000eoo`8000ioo`03 001oo`0000eoo`8000ioo`8000ioo`8001Eoo`006goo00<007ooOol037oo00<007oo00003Goo0P00 3Woo0P003Woo0P003Woo0P003Goo00<007oo00003Goo00<007oo00003Goo00<007oo00003Goo00<0 07oo00003Goo00<007oo00003Goo00<007oo00003Goo00<007oo00003Goo00<007oo00003Goo0P00 3Woo0P005Goo000KOol2000=Ool00`00Ool0000=Ool2000=Ool00`00Ool0000=Ool00`00Ool0000> Ool2000=Ool00`00Ool0000=Ool00`00Ool0000=Ool00`00Ool0000=Ool00`00Ool0000=Ool00`00 Ool0000=Ool00`00Ool0000=Ool00`00Ool0000=Ool00`00Ool0000=Ool2000>Ool2000EOol001]o o`8000eoo`03001oo`0000eoo`8000eoo`03001oo`0000eoo`03001oo`0000eoo`03001oo`0000eo o`03001oo`0000eoo`03001oo`0000eoo`03001oo`0000eoo`03001oo`0000eoo`03001oo`0000eo o`03001oo`0000eoo`03001oo`0000eoo`03001oo`0000aoo`04001oogoo000=Ool2000EOol001]o o`8000eoo`03001oo`0000aoo`03001oo`0000eoo`03001oo`0000eoo`04001oogoo000