(*^
::[ Information =
"This is a Mathematica Notebook file. It contains ASCII text, and can be
transferred by email, ftp, or other text-file transfer utility. It should
be read or edited using a copy of Mathematica or MathReader. If you
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everything from the line containing (*^ down to the line containing ^*)
into a plain text file. On some systems you may have to give the file a
name ending with ".ma" to allow Mathematica to recognize it as a Notebook.
The line below identifies what version of Mathematica created this file,
but it can be opened using any other version as well.";
FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2";
MacintoshStandardFontEncoding;
fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8, 24, "Times";
fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, "Times";
fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, "Times";
fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 18, "Times";
fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 14, "Times";
fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, "Times";
fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times";
fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5, 12, "Courier";
fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier";
fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5, 12, "Courier";
fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier";
fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5, 12, "Courier";
fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, "Courier";
fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, 10, "Geneva";
fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = leftheader, inactive, L2, 12, "Times";
fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, 12, "Times";
fontset = leftfooter, inactive, L2, 12, "Times";
fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times";
fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
paletteColors = 128; automaticGrouping; currentKernel;
]
:[font = input; preserveAspect]
ClearAll;
$DefaultFont = {"Times-Roman",10};
Needs["Graphics`Graphics`"];
c1 = 0.29; c2 = 0.32; c3 = 0.34;
K = 0.07; L1 = 1.07; r1 = K/(L1 GoldenRatio);
L2 = 80; r2 = K/(L2 GoldenRatio);
V[t_]:= 5 (8779 + 70560 t - 924000 t^2 + 3136000 t^3 - 3360000 t^4)/432;
v[t_]:= 350(10 t - 3)(20 t - 1)(7 - 20 t)/9;
plV = Plot[V[t],{t,0.28,0.35}];
plv = Plot[v[t],{t,0.28,0.35}];
opt = FindMinimum[-v[t],{t,0.32,0.33}];
topt = t/.opt[[2]];
a = -opt[[1]];
circ = Graphics[Disk[{topt,a},0.0005{1,1/r2}],
AspectRatio->Automatic];
ucirc = Graphics[Disk[{topt,V[topt]},0.0005{1,1/r1}],
AspectRatio->Automatic];
xticksua = Graphics[{Thickness[0.0012],Table[Line[{{0.28 + 0.01i,48.95},
{0.28 + 0.01i,48.975}}],{i,0,7}]}];
xticksub = Graphics[Table[Text[0.28 + 0.01i,{0.28 + 0.01i,48.91}],{i,0,7}]];
xticksla = Graphics[{Thickness[0.0012],Table[Line[{{0.28 + 0.01i,0},
{0.28 + 0.01i,0.85}}],{i,0,1}]}];
xtickslb = Graphics[{Thickness[0.0012],Table[Line[{{0.28 + 0.01i,0},
{0.28 + 0.01i,0.85}}],{i,3,6}]}];
xticksu = Join[Table[0.28 + 0.01i,{i,0,7}],{{topt,"s"}}];
yticksu = Join[{49,50},Table[{49+0.1i," "},{i,9}]];
yticksl = {-50,-25,0,25};
line1 = Graphics[{Dashing[{0.01,0.01}],Line[{{c1,0},{c1,V[c1]}}]}];
line2 = Graphics[{Dashing[{0.01,0.01}],Line[{{c2,0},{c2,V[c2]}}]}];
line3 = Graphics[{Dashing[{0.01,0.01}],Line[{{c3,0},{c3,V[c3]}}]}];
line4 = Graphics[{Dashing[{0.01,0.01}],Line[{{c1,0},{c1,v[c1]}}]}];
line5 = Graphics[{Dashing[{0.01,0.01}],Line[{{c2,0},{c2,v[c2]}}]}];
line6 = Graphics[{Dashing[{0.01,0.01}],Line[{{c3,0},{c3,v[c3]}}]}];
upper = Show[plV, ucirc,line1, line2, line3, xticksua,xticksub,
Graphics[{Thickness[0.0012],Line[{{0.28,48.95},{0.35,48.95}}]}],
AxesLabel->{"t","y"},
AxesOrigin->{0.275,48.95},
Ticks->{xticksu,yticksu},Axes->{False,True},
PlotRange -> {{0.28,0.35},{48.95,50.02}},
PlotLabel->FontForm["(a) y = V(t)",{"Courier",10}]];
lower = Show[plv, circ,line4, line5, line6, xticksla,xtickslb,
Graphics[{Thickness[0.0012],Line[{{0.28,0},{0.35,0}}]}],
Graphics[Text["s",{topt,-2}]],
AxesLabel->{"t","y"},
AxesOrigin->{0.275,-1},Axes->{False,True},
Ticks->{None,yticksl},
PlotRange -> {{0.28,0.35},{-51,29}},
PlotLabel->FontForm["(b) y = v(t) = V'(t)",{"Courier",10}]];
Show[GraphicsArray[{{upper},{lower}},PlotLabel->"Figure 14.1"]]
^*)