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maxsize = \"infinity\", \+ minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accen t = \"false\", font_style_name = \"2D Math\", size = \"14\", foregroun d = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mn(\"1 \"), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \+ \"false\", separator = \"true\", lspace = \"0em\", rspace = \"verythic kmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \+ \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \" false\", accent = \"false\", font_style_name = \"2D Math\", size = \"1 4\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typese tting:-mi(\"October\"), Typesetting:-mo(\"⁢\", form = \+ \"infix\", fence = \"false\", separator = \"true\", lspace = \"0em\", \+ rspace = \"verythickmathspace\", stretchy = \"false\", symmetric = \"f alse\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", \+ movablelimits = \"false\", accent = \"false\", font_style_name = \"2D \+ Math\", size = \"14\", foreground = \"[0,0,0]\", background = \"[255,2 55,255]\"), Typesetting:-mn(\"20\"), Typesetting:-mo(\",\", form = \"i nfix\", fence = \"false\", separator = \"true\", lspace = \"0em\", rsp ace = \"verythickmathspace\", stretchy = \"false\", symmetric = \"fals e\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", mov ablelimits = \"false\", accent = \"false\", font_style_name = \"2D Mat h\", size = \"14\", foreground = \"[0,0,0]\", background = \"[255,255, 255]\"), Typesetting:-mo(\"⁢\", form = \"\", fence = \" false\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", st retchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", min size = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Math\", size = \"14\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mn(\"2005 \"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6,-I#miGF $6#Q%TestF'-I#moGF$63Q1⁢F'/%%formGQ&infixF'/%&fenceGQ&f alseF'/%*separatorGQ%trueF'/%'lspaceGQ$0emF'/%'rspaceGQ3verythickmaths paceF'/%)stretchyGF8/%*symmetricGF8/%(maxsizeGQ)infinityF'/%(minsizeGQ \"1F'/%(largeopGF8/%.movablelimitsGF8/%'accentGF8/%0font_style_nameGQ( 2D~MathF'/%%sizeGQ#14F'/%+foregroundGQ([0,0,0]F'/%+backgroundGQ.[255,2 55,255]F'-I#mnGF$6#FKF/-F,6#Q(OctoberF'F/-Fin6#Q#20F'-F063Q\",F'F3F6F9 FFBFDFFFIFLFNFPF RFUFXFen-Fin6#Q%2005F'" }{TEXT 200 0 "" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 200 13 "Time: 50 min." }}}{EXCHG {PARA 207 "" 0 "" {TEXT 200 0 " " }}}{EXCHG {PARA 208 "" 0 "" {TEXT 200 66 "Use Maple, and webnotes/wo rksheets to solve the following problem." }}}{EXCHG {PARA 209 "" 0 "" {TEXT 200 0 "" }}}{EXCHG {PARA 210 "" 0 "" {TEXT 200 57 "Consider the \+ oscillator described by the Newton equation:" }}}{EXCHG {PARA 211 "" 0 "" {TEXT 200 0 "" }}}{EXCHG {PARA 212 "" 0 "" {TEXT 202 1 "x" }{TEXT 200 13 "''(t) + 0.05 " }{TEXT 203 1 "x" }{TEXT 200 2 "'(" }{TEXT 204 1 "t" }{TEXT 200 8 ") - 0.5 " }{TEXT 205 1 "x" }{TEXT 200 1 "(" }{TEXT 206 1 "t" }{TEXT 200 8 ") + 0.1 " }{TEXT 207 1 "x" }{TEXT 200 1 "(" } {TEXT 208 1 "t" }{TEXT 200 7 ")^3 = 0" }}}{EXCHG {PARA 213 "" 0 "" {TEXT 200 0 "" }}}{EXCHG {PARA 214 "" 0 "" {TEXT 200 94 "1) [20] Expla in the three force terms that appear in the equation. What effect do t hey have on" }}}{EXCHG {PARA 215 "" 0 "" {TEXT 200 28 "the mass? (whic h was set to " }{TEXT 209 1 "m" }{TEXT 200 4 "=1)." }}}{EXCHG {PARA 216 "" 0 "" {TEXT 200 0 "" }}}{EXCHG {PARA 217 "" 0 "" {TEXT 200 106 " 2) [30] Construct a graph of natural oscillations using as an intial c ondition that the mass is let go at " }{TEXT 210 1 "x" }{TEXT 200 4 "= 5. " }}}{EXCHG {PARA 218 "" 0 "" {TEXT 200 40 "Describe the behavior. \+ Graph separately " }{TEXT 211 1 "x" }{TEXT 200 1 "(" }{TEXT 212 1 "t" }{TEXT 200 6 ") and " }{TEXT 213 1 "x" }{TEXT 200 2 "'(" }{TEXT 214 1 "t" }{TEXT 200 2 ")." }}}{EXCHG {PARA 219 "" 0 "" {TEXT 200 0 "" }}} {EXCHG {PARA 220 "" 0 "" {TEXT 200 111 "3) [20] Measure the time it ta kes the mass to return to its maximum positive displacement for the fi rst swing. " }}}{EXCHG {PARA 221 "" 0 "" {TEXT 200 83 "Then repeat the measurement for a later cycle when the motion has almost died down." }}}{EXCHG {PARA 222 "" 0 "" {TEXT 200 0 "" }}}{EXCHG {PARA 223 "" 0 "" {TEXT 200 119 "4) [10]Now try initial conditions not far away from th e one given such that the solution looks qualitatively different." }}} {EXCHG {PARA 224 "" 0 "" {TEXT 200 0 "" }}}{EXCHG {PARA 225 "" 0 "" {TEXT 200 55 "5) [20] Produce phase-space graphs for both situations." }}}{EXCHG {PARA 226 "" 0 "" {TEXT 200 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 215 8 "Answers:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 216 2 "1)" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 200 96 "first term: the -0.05 x'(t) is a \+ drag force that counteracts the velocity (linear in the speed);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 200 107 "second term: the +0.5 x(t) is a \+ linear force in the displacement which pushes the mass away from the o rigin" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 51 "third term: -0.1x(t)^3 is a cubic restoring force." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 104 "The cubic restoring force dominates the linear force that pushes away from zero at sufficiently large x." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 334 "2) the graphs are do ne in the worksheet below. The behavior: the combination of a force th at pushes away from the origin with a force that restores, leads to tw o equilibrium points, symmetrically about 0, i.e., at x= +/- C. The va lue of C is found by asking where the mechanical force vanishes. (see \+ worksheet below at the beginning.)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 78 "3) about 6 seconds. A n accurate determination is given in the worksheet below." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 102 "4) changing x0=5 to x0=5.2 with zero intial velocity leads to the mass winding up on the opposite side" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart; Digits:=14:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "C:=solve(-0.5*x+0.1*x^3=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"CG6\"6%$\"\"!F'$\"/)*\\xz1OA!#8$!/)*\\xz1OAF*" }}} {EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Typesetting: -mi(\"There\"), Typesetting:-mo(\"⁢\", form = \"infix\" , fence = \"false\", separator = \"false\", lspace = \"thickmathspace \", rspace = \"thickmathspace\", stretchy = \"false\", symmetric = \"f alse\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", \+ movablelimits = \"false\", accent = \"false\", font_style_name = \"2D \+ Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255, 255,255]\"), Typesetting:-mi(\"are\"), 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separator = \"f alse\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", symm etric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \+ \"false\", movablelimits = \"false\", accent = \"false\", font_style_n ame = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", backgroun d = \"[255,255,255]\"), Typesetting:-mi(\"places\"), Typesetting:-mo( \"⁢\", form = \"infix\", fence = \"false\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", \+ symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeo p = \"false\", movablelimits = \"false\", accent = \"false\", font_sty le_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", backg round = \"[255,255,255]\"), Typesetting:-mi(\"where\"), Typesetting:-m o(\"⁢\", form = \"infix\", fence = \"false\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\" , symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", larg eop = \"false\", 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Typesetting:-mi(\"can\"), Typesetting: -mo(\"⁢\", form = \"infix\", fence = \"false\", separat or = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false \", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", font _style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", b ackground = \"[255,255,255]\"), Typesetting:-mi(\"settle\"), Typesetti ng:-mo(\"⁢\", form = \"infix\", fence = \"false\", sepa rator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"fa lse\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", f ont_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\" , background = \"[255,255,255]\"), Typesetting:-mi(\"when\"), Typesett ing:-mo(\"⁢\", form = \"infix\", fence = \"false\", sep arator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"f alse\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\" , largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+ font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0] \", background = \"[255,255,255]\"), Typesetting:-mi(\"the\"), Typeset ting:-mo(\"⁢\", form = \"infix\", fence = \"false\", se parator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \" false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1 \", largeop = \"false\", movablelimits = \"false\", accent = \"false\" , font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0 ]\", background = \"[255,255,255]\"), Typesetting:-mi(\"drag\"), Types etting:-mo(\"⁢\", form = \"infix\", fence = \"false\", \+ separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \+ \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \" 1\", largeop = \"false\", movablelimits = \"false\", accent = \"false \", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0 ,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"force\"), Ty pesetting:-mo(\"⁢\", form = \"infix\", fence = \"false \", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretch y = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize \+ = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"fa lse\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[ 0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"removes\" ), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"f alse\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", str etchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", mins ize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \+ \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"its\" ), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"f alse\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", str etchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", mins ize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \+ \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"mecha nical\"), Typesetting:-mo(\"⁢\", form = \"infix\", fenc e = \"false\", separator = \"false\", lspace = \"0em\", rspace = \"0em \", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity \", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", font_style_name = \"2D Input\", size = \"12\", fore ground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi (\"energy\"), Typesetting:-mo(\"⁢\", form = \"infix\", \+ fence = \"false\", separator = \"false\", lspace = \"0em\", rspace = \+ \"0em\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infi nity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false \", accent = \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesettin g:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"imparted\"), Typesettin g:-mo(\"⁢\", form = \"infix\", fence = \"false\", separ ator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"fal se\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", \+ largeop = \"false\", movablelimits = \"false\", accent = \"false\", fo nt_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"by\"), Typesetting :-mo(\"⁢\", form = \"infix\", fence = \"false\", separa tor = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"fals e\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", l argeop = \"false\", movablelimits = \"false\", accent = \"false\", fon t_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", \+ background 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= \"1\", largeo p = \"false\", movablelimits = \"false\", accent = \"false\", font_sty le_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", backg round = \"[255,255,255]\"), Typesetting:-mi(\"be\"), Typesetting:-mo( \"⁢\", form = \"infix\", fence = \"false\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", \+ symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeo p = \"false\", movablelimits = \"false\", accent = \"false\", font_sty le_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", backg round = \"[255,255,255]\"), Typesetting:-mi(\"used\"), Typesetting:-mo (\".\", form = \"infix\", fence = \"false\", separator = \"false\", ls pace = \"0em\", rspace = \"0em\", stretchy = \"false\", symmetric = \" false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255 ,255,255]\"), Typesetting:-mo(\"⁢\", form = \"infix\", \+ fence = \"false\", separator = \"true\", lspace = \"0em\", rspace = \" verythickmathspace\", stretchy = \"false\", symmetric = \"false\", max size = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimi ts = \"false\", accent = \"false\", font_style_name = \"2D Input\", si ze = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\") , Typesetting:-mi(\"creating\"), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"false\", separator = \"true\", lspace = \+ \"0em\", rspace = \"verythickmathspace\", stretchy = \"false\", symmet ric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \" false\", movablelimits = \"false\", accent = \"false\", font_style_nam e = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background \+ = \"[255,255,255]\"), Typesetting:-mi(\"a\"), Typesetting:-mo(\"&Invis ibleTimes;\", form = \"infix\", fence = \"false\", separator = \"true \", lspace = \"0em\", rspace = \"verythickmathspace\", stretchy = \"fa lse\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", f ont_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\" , background = \"[255,255,255]\"), Typesetting:-mi(\"zoomed\"), Typese tting:-mo(\"⁢\", form = \"infix\", fence = \"false\", s eparator = \"true\", lspace = \"0em\", rspace = \"verythickmathspace\" , stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", acce nt = \"false\", font_style_name = \"2D Input\", size = \"12\", foregro und = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\" graph\"), Typesetting:-mo(\"⁢\", form = \"infix\", fenc e = \"false\", separator = \"true\", lspace = \"0em\", rspace = \"very thickmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Ty pesetting:-mi(\"which\"), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"false\", separator = \"true\", lspace = \"0em\", rspace = \"verythickmathspace\", stretchy = \"false\", symmetric = \" false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255 ,255,255]\"), Typesetting:-mi(\"allows\"), Typesetting:-mo(\"&Invisibl eTimes;\", form = \"infix\", fence = \"false\", separator = \"true\", \+ lspace = \"0em\", rspace = \"verythickmathspace\", stretchy = \"false \", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", font _style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", b ackground = \"[255,255,255]\"), Typesetting:-mi(\"to\"), Typesetting:- mo(\"⁢\", form = \"infix\", fence = \"false\", separato r = \"true\", lspace = \"0em\", rspace = \"verythickmathspace\", stret chy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsiz e = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \" false\", font_style_name = \"2D Input\", size = \"12\", foreground = \+ \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"point \"), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \+ \"false\", separator = \"true\", lspace = \"0em\", rspace = \"verythic kmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \+ \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \" false\", accent = \"false\", font_style_name = \"2D Input\", size = \" 12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Types etting:-mi(\"and\"), Typesetting:-mo(\"⁢\", form = \"in fix\", fence = \"false\", separator = \"true\", lspace = \"0em\", rspa ce = \"verythickmathspace\", stretchy = \"false\", symmetric = \"false \", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", mova blelimits = \"false\", accent = \"false\", font_style_name = \"2D Inpu t\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255, 255]\"), Typesetting:-mi(\"click\"), Typesetting:-mo(\"&InvisibleTimes ;\", form = \"infix\", fence = \"false\", separator = \"true\", lspace = \"0em\", rspace = \"verythickmathspace\", stretchy = \"false\", sym metric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", font_style_ name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", backgrou nd = \"[255,255,255]\"), Typesetting:-mi(\"and\"), Typesetting:-mo(\"& InvisibleTimes;\", form = \"infix\", fence = \"false\", separator = \" true\", lspace = \"0em\", rspace = \"verythickmathspace\", stretchy = \+ \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \" 1\", largeop = \"false\", movablelimits = \"false\", accent = \"false \", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0 ,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"read\"), Typ esetting:-mo(\"⁢\", form = \"infix\", fence = \"false\" , separator = \"true\", lspace = \"0em\", rspace = \"verythickmathspac e\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity \", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", font_style_name = \"2D Input\", size = \"12\", fore ground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mf enced(Typesetting:-mrow(Typesetting:-mi(\"x\"), Typesetting:-mo(\",\", form = \"infix\", fence = \"false\", separator = \"true\", lspace = \+ \"0em\", rspace = \"verythickmathspace\", stretchy = \"false\", symmet ric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \" false\", movablelimits = \"false\", accent = \"false\", font_style_nam e = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background \+ = \"[255,255,255]\"), Typesetting:-mi(\"y\"))), Typesetting:-mo(\"&Inv isibleTimes;\", form = \"infix\", fence = \"false\", separator = \"fal se\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", symmet ric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \" false\", movablelimits = \"false\", accent = \"false\", font_style_nam e = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background \+ = \"[255,255,255]\"), Typesetting:-mi(\"is\"), Typesetting:-mo(\"&Invi sibleTimes;\", form = \"infix\", fence = \"false\", separator = \"fals e\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", symmetr ic = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"f alse\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"one\"), Typesetting:-mo(\"&Invi 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\"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Ty pesetting:-mi(\"Another\"), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"false\", separator = \"true\", lspace = \"0em \", rspace = \"verythickmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false \", movablelimits = \"false\", accent = \"false\", font_style_name = \+ \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \" [255,255,255]\"), Typesetting:-mi(\"option\"), Typesetting:-mo(\"&Invi sibleTimes;\", form = \"infix\", fence = \"false\", separator = \"true \", lspace = \"0em\", rspace = \"verythickmathspace\", stretchy = \"fa lse\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", f ont_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\" , background = \"[255,255,255]\"), Typesetting:-mi(\"is\"), Typesettin g:-mo(\"⁢\", form = \"infix\", fence = \"false\", separ ator = \"true\", lspace = \"0em\", rspace = \"verythickmathspace\", st retchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", min size = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Input\", size = \"12\", foreground \+ = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"to\" ), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"f alse\", separator = \"true\", lspace = \"0em\", rspace = \"verythickma thspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \"in finity\", minsize = \"1\", largeop = \"false\", movablelimits = \"fals e\", accent = \"false\", font_style_name = \"2D Input\", size = \"12\" , foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetti ng:-mi(\"create\"), Typesetting:-mo(\"⁢\", form = \"inf ix\", fence = \"false\", separator = \"true\", lspace = \"0em\", rspac e = \"verythickmathspace\", stretchy = \"false\", symmetric = \"false \", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", mova blelimits = \"false\", accent = \"false\", font_style_name = \"2D Inpu t\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255, 255]\"), Typesetting:-mi(\"a\"), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"false\", separator = \"true\", lspace = \+ \"0em\", rspace = \"verythickmathspace\", stretchy = \"false\", symmet ric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \" false\", movablelimits = \"false\", accent = \"false\", font_style_nam e = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background \+ = \"[255,255,255]\"), Typesetting:-mi(\"sequence\"), Typesetting:-mo( \"⁢\", form = \"infix\", fence = \"false\", separator = \"true\", lspace = \"0em\", rspace = \"verythickmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"fal se\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0 ,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"of\"), Typ esetting:-mo(\"⁢\", form = \"infix\", fence = \"false\" , separator = \"true\", lspace = \"0em\", rspace = \"verythickmathspac e\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity \", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", font_style_name = \"2D Input\", size = \"12\", fore ground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi (\"points\"), Typesetting:-mo(\"⁢\", form = \"infix\", \+ fence = \"false\", separator = \"true\", lspace = \"0em\", rspace = \" verythickmathspace\", stretchy = \"false\", symmetric = \"false\", max size = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimi ts = \"false\", accent = \"false\", font_style_name = \"2D Input\", si ze = \"12\", foreground = 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separat or = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false \", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", font _style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", b ackground = \"[255,255,255]\"), Typesetting:-mi(\"which\"), Typesettin g:-mo(\"⁢\", form = \"infix\", fence = \"false\", separ ator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"fal se\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", \+ largeop = \"false\", movablelimits = \"false\", accent = \"false\", fo nt_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"could\"), Typesett ing:-mo(\"⁢\", form = \"infix\", fence = \"false\", sep arator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"f alse\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\" , largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+ font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0] \", background = \"[255,255,255]\"), Typesetting:-mi(\"be\"), Typesett ing:-mo(\"⁢\", form = \"infix\", fence = \"false\", sep arator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"f alse\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\" , largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+ font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0] \", background = \"[255,255,255]\"), Typesetting:-mi(\"refined\"), Typ esetting:-mo(\"⁢\", form = \"infix\", fence = \"false\" , separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy \+ = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \+ \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"fals e\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0, 0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"to\"), Type setting:-mo(\"⁢\", form = \"infix\", fence = \"false\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \+ \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"fals e\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0, 0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"higher\"), \+ Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"fals e\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretc hy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"f alse\", font_style_name = \"2D Input\", size = \"12\", foreground = \" [0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"precisio n\"), Typesetting:-mo(\".\", form = \"infix\", fence = \"false\", sepa rator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"fa lse\", 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\"false\", font_style_name \+ = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \+ \"[255,255,255]\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_sys libGF'6+-I#miGF$6#Q-SuspiciouslyF'-I#moGF$63Q1⁢F'/%%for mGQ&infixF'/%&fenceGQ&falseF'/%*separatorGF8/%'lspaceGQ$0emF'/%'rspace GF=/%)stretchyGF8/%*symmetricGF8/%(maxsizeGQ)infinityF'/%(minsizeGQ\"1 F'/%(largeopGF8/%.movablelimitsGF8/%'accentGF8/%0font_style_nameGQ)2D~ InputF'/%%sizeGQ#12F'/%+foregroundGQ([0,0,0]F'/%+backgroundGQ.[255,255 ,255]F'-F,6#Q&closeF'F/-F,6#Q#toF'F/-I#mnGF$6#Q\"2F'-F,6#Q#PiF'-F063Q \".F'F3F6F9F;F>F@FBFDFGFJFLFNFPFSFVFY" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "V(107.9),V(101.6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 $$!3KZc#)f73i*)!#?$\"3h?&Q?FFS/'F%" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Typesetting:-mi(\"A\"), Typesetting:- mo(\"⁢\", form = \"infix\", fence = \"false\", separato r = \"false\", lspace = \"verythinmathspace\", rspace = \"verythinmath space\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infi nity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false \", accent = \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesettin g:-mi(\"root\"), Typesetting:-mo(\"⁢\", form = \"infix \", fence = \"false\", separator = \"false\", lspace = \"verythinmaths pace\", rspace = \"verythinmathspace\", stretchy = \"false\", symmetri c = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"fa lse\", movablelimits = \"false\", accent = \"false\", font_style_name \+ = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \+ \"[255,255,255]\"), Typesetting:-mi(\"search\"), Typesetting:-mo(\"&In visibleTimes;\", form = \"infix\", fence = \"false\", separator = \"fa lse\", lspace = \"verythinmathspace\", rspace = \"verythinmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", \+ minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accen t = \"false\", font_style_name = \"2D Input\", size = \"12\", foregrou nd = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"w ill\"), Typesetting:-mo(\"⁢\", form = \"infix\", fence \+ = \"false\", separator = \"false\", lspace = \"verythinmathspace\", rs pace = \"verythinmathspace\", stretchy = \"false\", symmetric = \"fals e\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", mov ablelimits = \"false\", accent = \"false\", font_style_name = \"2D Inp ut\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255 ,255]\"), Typesetting:-mi(\"determine\"), Typesetting:-mo(\"&Invisible Times;\", form = \"infix\", fence = \"false\", separator = \"false\", \+ lspace = \"verythinmathspace\", rspace = \"verythinmathspace\", stretc hy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"f alse\", font_style_name = \"2D Input\", size = \"12\", foreground = \" [0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"the\"), \+ Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"fals e\", separator = \"false\", lspace = \"verythinmathspace\", rspace = \+ \"verythinmathspace\", stretchy = \"false\", symmetric = \"false\", ma xsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelim its = \"false\", accent = \"false\", font_style_name = \"2D Input\", s ize = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\" ), Typesetting:-mi(\"times\"), Typesetting:-mo(\"⁢\", f orm = \"infix\", fence = \"false\", separator = \"false\", lspace = \" verythinmathspace\", rspace = \"verythinmathspace\", stretchy = \"fals e\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", l argeop = \"false\", movablelimits = \"false\", accent = \"false\", fon t_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", \+ background = \"[255,255,255]\"), Typesetting:-mi(\"where\"), Typesetti ng:-mo(\"⁢\", form = \"infix\", fence = \"false\", sepa rator = \"false\", lspace = \"verythinmathspace\", rspace = \"verythin mathspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \" infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"fa lse\", accent = \"false\", font_style_name = \"2D Input\", size = \"12 \", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typeset ting:-mi(\"the\"), Typesetting:-mo(\"⁢\", form = \"infi x\", fence = \"false\", separator = \"false\", lspace = \"verythinmath space\", rspace = \"verythinmathspace\", stretchy = \"false\", symmetr ic = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"f alse\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"velocity\"), Typesetting:-mo(\" ⁢\", form = \"infix\", fence = \"false\", separator = \+ \"false\", lspace = \"verythinmathspace\", rspace = \"verythinmathspac e\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity \", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", font_style_name = \"2D Input\", size = \"12\", fore ground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi (\"vanishes\"), Typesetting:-mo(\"!\", form = \"infix\", fence = \"fal se\", separator = \"false\", lspace = \"verythinmathspace\", rspace = \+ \"verythinmathspace\", stretchy = \"false\", symmetric = \"false\", ma xsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelim its = \"false\", accent = \"false\", font_style_name = \"2D Input\", s ize = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\" ));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'68-I#miGF$6 #Q\"AF'-I#moGF$63Q1⁢F'/%%formGQ&infixF'/%&fenceGQ&false F'/%*separatorGF8/%'lspaceGQ2verythinmathspaceF'/%'rspaceGF=/%)stretch yGF8/%*symmetricGF8/%(maxsizeGQ)infinityF'/%(minsizeGQ\"1F'/%(largeopG 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" 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Typesetting:-mi(\"We\"), Typesetting:-mo(\"&Invisib leTimes;\", form = \"infix\", fence = \"false\", separator = \"false\" , lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", symmetric \+ = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"fals e\", movablelimits = \"false\", accent = \"false\", font_style_name = \+ \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \" [255,255,255]\"), Typesetting:-mi(\"are\"), Typesetting:-mo(\"&Invisib leTimes;\", form = \"infix\", fence = \"false\", separator = \"false\" , lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", symmetric \+ = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"fals e\", movablelimits = \"false\", accent = \"false\", font_style_name = \+ \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \" [255,255,255]\"), Typesetting:-mi(\"above\"), Typesetting:-mo(\"&Invis ibleTimes;\", form = \"infix\", fence = \"false\", separator = \"false \", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", symmetri c = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"fa lse\", movablelimits = \"false\", accent = \"false\", font_style_name \+ = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \+ \"[255,255,255]\"), Typesetting:-mi(\"Pi\"), Typesetting:-mo(\".\", fo rm = \"infix\", fence = \"false\", separator = \"false\", lspace = \"0 em\", rspace = \"0em\", stretchy = \"false\", symmetric = \"false\", m axsize = \"infinity\", minsize = \"1\", largeop = \"false\", movableli mits = \"false\", accent = \"false\", font_style_name = \"2D Input\", \+ size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255] \"), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \+ \"false\", separator = \"false\", lspace = \"thickmathspace\", rspace \+ = \"thickmathspace\", stretchy = \"false\", symmetric = \"false\", max size = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimi ts = \"false\", accent = \"false\", font_style_name = \"2D Input\", si ze = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\") , Typesetting:-mi(\"Let\"), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"false\", separator = \"false\", lspace = \"thi ckmathspace\", rspace = \"thickmathspace\", stretchy = \"false\", symm etric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \+ \"false\", movablelimits = \"false\", accent = \"false\", font_style_n ame = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", backgroun d = \"[255,255,255]\"), Typesetting:-mi(\"us\"), Typesetting:-mo(\"&In visibleTimes;\", form = \"infix\", fence = \"false\", separator = \"fa lse\", lspace = \"thickmathspace\", rspace = \"thickmathspace\", stret chy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsiz e = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \" false\", font_style_name = \"2D Input\", size = \"12\", foreground = \+ \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"check \"), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \+ \"false\", separator = \"false\", lspace = \"thickmathspace\", rspace \+ = \"thickmathspace\", stretchy = \"false\", symmetric = \"false\", max size = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimi ts = \"false\", accent = \"false\", font_style_name = \"2D Input\", si ze = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\") , Typesetting:-mi(\"at\"), Typesetting:-mo(\"⁢\", form \+ = \"infix\", fence = \"false\", separator = \"false\", lspace = \"thic kmathspace\", rspace = \"thickmathspace\", stretchy = \"false\", symme tric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \+ \"false\", movablelimits = \"false\", accent = \"false\", font_style_n ame = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", backgroun d = \"[255,255,255]\"), Typesetting:-mi(\"a\"), Typesetting:-mo(\"&Inv isibleTimes;\", form = \"infix\", fence = \"false\", separator = \"fal se\", lspace = \"thickmathspace\", rspace = \"thickmathspace\", stretc hy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"f alse\", font_style_name = \"2D Input\", size = \"12\", foreground = \" [0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"later\") , Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"fa lse\", separator = \"false\", lspace = \"thickmathspace\", rspace = \" thickmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Ty pesetting:-mi(\"time\"), Typesetting:-mo(\":\", form = \"infix\", fenc e = \"false\", separator = \"false\", lspace = \"thickmathspace\", rsp ace = \"thickmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movable limits = \"false\", accent = \"false\", font_style_name = \"2D Input\" , size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255 ]\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'69-I#miG F$6#Q#WeF'-I#moGF$63Q1⁢F'/%%formGQ&infixF'/%&fenceGQ&fa lseF'/%*separatorGF8/%'lspaceGQ$0emF'/%'rspaceGF=/%)stretchyGF8/%*symm etricGF8/%(maxsizeGQ)infinityF'/%(minsizeGQ\"1F'/%(largeopGF8/%.movabl elimitsGF8/%'accentGF8/%0font_style_nameGQ)2D~InputF'/%%sizeGQ#12F'/%+ foregroundGQ([0,0,0]F'/%+backgroundGQ.[255,255,255]F'-F,6#Q$areF'F/-F, 6#Q&aboveF'F/-F,6#Q#PiF'-F063Q\".F'F3F6F9F;F>F@FBFDFGFJFLFNFPFSFVFY-F0 63F2F3F6F9/F " 0 "" {MPLTEXT 1 0 30 "t1:=fsolve(V(t)=0,t=200.. 205);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#t1G6\"$\"/NKGdCC?!#6" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "t2:=fsolve(V(t)=0,t=205..210 );" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#t2G6\"$\"/X-,J5(3#!#6" }}} {EXCHG {PARA 0 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\"[255,255,255]\"), Typesetting:-mi(\"indeed\"), Typesetting:-mo(\"&In visibleTimes;\", form = \"infix\", fence = \"false\", separator = \"fa lse\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", symme tric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \+ \"false\", movablelimits = \"false\", accent = \"false\", font_style_n ame = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", backgroun d = \"[255,255,255]\"), Typesetting:-mi(\"getting\"), Typesetting:-mo( \"⁢\", form = \"infix\", fence = \"false\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", \+ symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeo p = \"false\", movablelimits = \"false\", accent = \"false\", font_sty le_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", backg round = \"[255,255,255]\"), Typesetting:-mi(\"closer\"), Typesetting:- mo(\"⁢\", form = \"infix\", fence = \"false\", separato r = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false \", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", font _style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", b ackground = \"[255,255,255]\"), Typesetting:-mi(\"to\"), Typesetting:- mo(\"⁢\", form = \"infix\", fence = \"false\", separato r = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false \", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", font _style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", b ackground = \"[255,255,255]\"), Typesetting:-mn(\"2\"), Typesetting:-m i(\"Pi\"), Typesetting:-mo(\"⁢\", form = \"infix\", fen ce = \"false\", separator = \"false\", lspace = \"0em\", rspace = \"0e m\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity \", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", font_style_name = \"2D Input\", size = \"12\", fore ground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi (\"for\"), Typesetting:-mo(\"⁢\", form = \"infix\", fen ce = \"false\", separator = \"false\", lspace = \"0em\", rspace = \"0e m\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity \", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", font_style_name = \"2D Input\", size = \"12\", fore ground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi (\"the\"), Typesetting:-mo(\"⁢\", form = \"infix\", fen ce = \"false\", separator = \"false\", lspace = \"0em\", rspace = \"0e m\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity \", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", font_style_name = \"2D Input\", size = \"12\", fore ground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi (\"period\"), Typesetting:-mo(\".\", form = \"infix\", fence = \"false \", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretch y = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize \+ = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"fa lse\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[ 0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mo(\"&Invisibl eTimes;\", form = \"infix\", fence = \"false\", separator = \"true\", \+ lspace = \"0em\", rspace = \"verythickmathspace\", stretchy = \"false \", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", font _style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", b ackground = \"[255,255,255]\"), Typesetting:-mi(\"As\"), Typesetting:- mo(\"⁢\", form = \"infix\", fence = \"false\", separato r = \"true\", lspace = \"0em\", rspace = \"verythickmathspace\", stret chy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsiz e = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \" false\", font_style_name = \"2D Input\", size = \"12\", foreground = \+ \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"the\") , Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"fa lse\", separator = \"true\", lspace = \"0em\", rspace = \"verythickmat hspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \"inf inity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false \", accent = \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesettin g:-mi(\"oscillation\"), Typesetting:-mo(\"⁢\", form = \+ \"infix\", fence = \"false\", separator = \"true\", lspace = \"0em\", \+ rspace = \"verythickmathspace\", stretchy = \"false\", symmetric = \"f alse\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", \+ movablelimits = \"false\", accent = \"false\", font_style_name = \"2D \+ Input\", 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