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 8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈ۭm浍浭m䵍䵩m嵍`"L ŵ8ŵH ~(`# d ֠z# u`%%$%2VV]O+1,1V8]в׳؀++%*+%*+&,8VV1VVW^*$*$*++11UVVV{]Э׳m%%%***$$%$2W]*+*+++1UVWWЬѲ+%+%**%%%+2VVW+1+1PVW|в++%+%+PWVV1**%%%$$2zO*+++OUVV{]+*+%%%%%*%%+VWV^++,,22\{++%*+%++PVW22V\s*%++OP22VV{]Ь*+%%$2\|+*+++122V\{г~+%+%+*++VWdX2P\π%%%%%++P,PUV\\ѭ׳s+%*%$$$P{~++*+O1P2V\]ѳm++%%%+2V{Vy++1P2V{ѳ؀++*+%%++2]WcW22W\+%%*O,1PPVV{]Ьвy*+%*%%$%+VWW+,,1V3Wѭ؀+%+*+%*++V]XydY2VWm%*%*+,,,22P\W]^ѭ׳+*%%$$%$V]++%+11P2VW\Ѳץs*+*%$%$$%%,2VVO,+OPVV{Ьѳ++*]гѲѳ%*+%$%$$VO+++OP1VV\]+%*%%$%%$*%+VW^XsO,,2PWWѭ+%+*+%+,3cc؀2c2V{*+++OP22VV\Ѳ׳s*+*%%$$$Vc+++,,1PVV{]V\+%+*+%+1Vв,P{%*++,+P1PPVWW]вѳ*+%*%$$%Wy++O,1PPVV{]ѬѳO*+%*$*%%+2V]c؀+11P2V\вѲ؀+%+*+*+,2cz3c2W~+%%++11P22VV{$$s+1,1P22VV{׳s+*+%*$*%%+VW]+OOUUVzѬ׳؀+*++%+1VPV؀+%++,+P,P2PVz{ѳ%%*%%%c+++OP1UVV\{s+%%%%%PV]c+11PVcyV^cVV1OOO1OP1UVVWW{Э%%$$$$cs+OP,222VV{]~++%$%%$$**+2V]c,,12PV\]в֥++%*+%*+1Q^ЬyVs+,+,,,,1UVUz\вѳ+%%*$$%%$**1VW]X؀,,22P\W]~+++%+%,,WвѳcPVcPzVUP,,,1P1UVV\\ЬѲs$WOP,1P222VV{]ѭץs++*+%$%%%1VWc؀+P1PVV\|++*+%*+%,,]ѭѲ׳s%*%%$%V]VUUUUPUVVV{]+++%*%$%%+VVWyOPPUVWW^Ьy++%*+%12]вXsVY2VVUP1OP121V2Vz{$V,21PP222VV\m++%$+1\ѭ׳ץV1VW2PVUUOP1P1UVVV\ѭ+*%%VW{\UV222PVVW\в~+%+%%%%%,VWVyOUUVVV\ѳs+*+%+%OV]Э׳W,VX2VUV1P1OP21VPWW]+%%**%*$%%+,VWЬV]ɀ2UVV2VWWѳ+%+**+++P]׳VPWW22V2P1P1P1UVVWW{ЬЭѲ~++%%$$$$$%Pz{WUVPUV2VVW]ѳN+*+%%*,2V{V1UV2U\V\ѳO%+*+%+Э~+%*%$$$$%2\WVVVPV2VVV{]Э׳s+*%%%%+,VWЬвѲV\VVVVVVW\ײ؀+%*+*++,2|Э׳VtP{V22UV1P1P21V2V\]]ѳ֥+%+%%$$$%2\\\VUV2PVVV\{ѳ++2VϬЭѭV]1WWV1V2PP21P1V2VVW]ѳ+*+%$$$$%+2WV\VUVUVVVV{в+*%%$%%+PV\ЬвѲѳVW]VWUVWV\ѳ+*+*+++V]гV^tPzV22PUUP1P21V2Vz{%+2V]Ѳѳ2z{{WVWVV\]^Ѳ~++*+%*++1WЭѲѳV]yV\]V1V2221P21V2VV\Ь~*+%$,2VzVVVV2VVVW\+**%**%*%1VVѳP{]]WVVVV\\ѳ++%+%*$%$$++2VVzVV2VVVV\Э++****%*+2V\Ϭ׳2z{\zzVVz\]ץ++*+%*++1VV\VV\]V^1UV221P21V2VV{Э****+$$$,2VWVVVUVVVV\{ЬѲm+**%%%%%%%+P2\{ЭѲ׳++%*%%*2VWW\O%++++28]ѳ2WW{2z1P222UV\W+*%$+,22VzЬЭѳ**+%*$%$22VVWV{]֥~+%+*%%+22zѲ׳+++%%%%%*$$$$$22VV\W\ѭ؀+**%%%,1VzвѲ׳s++*%%*%2VWW\++++22{Э2WW2z1P222V2z]^Ь%*%$*+1PUWVѳ~***+$%$22VV\V{ѳ+**+122VWW{г~*+%%*$$$22VVz\{s%*+*%%,,2\]cЬѳ׳++*%%%$$$%2VWW]s+++O1V]Ѭ~++*+2W\2z1P22PVVVѥs%%$$%+1PVVW]Эѳ*+1P22UVV{]ץm+%%%++PPVWW{вs%%%%22VVz\؀+%*%+%OUV{]Э׳+*+***%%*$$$2VW\{O++*+OPV{y+*+*%*2W\2z1P22PVV\{Հ**%%$$$%+г׳y%+*+*%%*2\]c2{^1P22V2\\ѳ*+$%$$11V2\W{ѥm%%%%%%*$$22VWV{]ѥ~++%**++22\]Ѳm+%+%%%%%2V\\+++,+VVѭѳ*++%%+%2\\2z%$$%2V\]^ѥs+*++OPVѲ+%+%*+%2\]P{c1PPPVQV{ѥs*%%%+1PV3VЭгs***$%$22V\W\ѱO%**%%+1PV{|вѲ׳+%+%%*%$%$$$%2V\\y++%+O23W%%%%,,PWWЬ+++%$%$%2V\{؀+%++11V\y*++*%%*+2\]P{1PPPVVW]Ѳ**%$$$%*,,1VVWWЭm$2PVzW]ѥ~++****+,1V\{ЬѲ++*+*%*%$$%$2PWV{]؀+%+%*+OUV\{ѳ~+*++*%$%$%%2Vz*+++1PV]Э+%+%*+*2\{QW1PPPVV\׳m%%%$$*+,,PVVzcЬ%%%%%%%$$$$$2PVz\{s+s%*%$%+,,2PWW\Э׳m++*%*%$$2P\V{s*++,1V\{ѳץy%+++$%$$$%%2Vz++++122{Эץ+++%+*++2\QW1PPUVWW^Ѳ+%$%$%%1,22V\]]Ѳ֬Ѳץ+++%%%*++2zV\1PPVVV{Ь*%%*+OP2VV\{Ѳ++*%%%$$2PzW\++%*%%++P2WWѲ+%%%$$$$%*2V{]؀++++OPVѳ++%*++%%+2zVW1PPVU\\m+%*+%$%%%+2W\O+++12V\+%+*%*+%+12{cV]1PUVVW]ѥs%%$$$$%+1P2VV{]вѭ׳m++%%$2VV\{%+%+,1VW\Эѳץs+%***%$$$%%+2WWѥs+++,1VW$%%2VV{|؀+%++OUV\]׫+*+%%%$%,2W]++++PP\ѭץ+++%%*++2P{V]1PUVVzѳ***$$+OP1VV\{вѲѭ׳s++$%%$$2VV\ѫ++%%+,22W\UVVV{*%%O1UV8V{]гѲs*+%+%2VW\s%+*+122V{]вѭm++%%$%,2\]y+1+P2W]m+*+++%%+,QWV]1UV2\\ѥm+%%+,,PPV\{]Ьѳ~+*+%,V2z++,+PVV+*+*%*+%+UV]V1UVVW]m%*%%++1PPVV\{Ь~+%*+%$2VW]ѥ؀%+%*+11PV\{г׳s++*%$%$$%+22\؀++,+P2VѲץ++%+%%*++VVWV^12V{^++%++P2V\{вѳ+%+%%$$%*1V2{cy++,,22{ѭs+*+**+%+PV]V1UVV\~+%$$%%,,1UVV\{Эs%%**+$$$$2V\m+*+%,,1VWWѳ~++%%*%%%%%V2z{y%$$%,+PPPWV{{s%%*+$$$$$$$$2V{y*+%+&+1UVW\вѲm+****%*$%%+VQW+++122W]+*+%*+%,2^V^V1V2WWѲ+$%%++P1UVV{]%%*+$$$THE SCREEN"{x 9,78:AB{ A$"@WITH SMALL INITIAL @U@' AND @U."O{ 9,88:A{ A$" S@PHERICALLY SYMMETRICAL 3-DIMENSIONAL"{ 9,100:A{ A$"@WELLS CAN BE ANALYZED USING 'CENTRIFUGAL"{ 9,110:A| A$"@POTENTIAL.' @F@OR EXAMPLE, ENERGY LEV FORBIDDEN REGIONS."!z( 9,36:ASz2 A$" W@E USUALLY TAKE ADVANTAGE OF SYMMETRY"`z< 9,48:AzF A$"@TO DISPLAY ONLY THE RIGHT HALF OF THE"zP 9,58:AzZ A$"@WELL. @A@N ASYMMETRICAL WELL CAN BE"zd 9,68:A {n A$"@PLACED NEAR THE LEFT SIDE OF ----------------PAGE 3#y :3Wy A$" U@ CURVES TOWARD THE @X@-AXIS IN CLASSI-"jy 9,6:A6981:Ay A$"@CALLY ALLOWED REGIONS, THAT IS, REGIONS"y 9,16:Ay A$"@WHERE @E > V(X); @AND @U@ CURVES AWAY FROM"y 9,26:Az A$"@THE AXIS IN$S$:S$;Sx S$"X"X$"X"Ĺ16304,0:16299,0:T$"G":S$:16300,0:230,32:2420x S$"E"S$"L"S$"M"S$"S"S$"U"S$"X"S$(13)S$","S$" "ıx S$"T"T$"T"Ĺ16304,0:T$"G":2420x S$"T"ĉ:T$"T"x S$(27)ī10:INTROx 2420y w$ X$S$,w. LLOL(MMO)Oī1250:GRIDFw8 S$"S"ī1610:PLOT UVwB 1250:GRIDrwL ------------GET DIGITS}wV A$" "w` 16368,0wj S$"X"ī2450wt S$w~ S$(8)(A$)1A$(A$,(A$)1):S$" "S$; x S$"."S$"9"S$"/"(A$)ALA$AvA$" "ĺL;:2310"vL(A$),v2310>v","24)"M=";GvAL4]v2380:GET DIGITSsvA$" "ĺM;:2270vM(A$)vM0ī2220v2320vS$"U"ī1990vS$"L"ī2160v S$"M"ī2220v S$"E"ī1910v 16304,0:T$"G":GRAPHICS0:GET DIGITS$uA$" "ĺUO;:23101u UO(A$);u2310Nu ","10)"UA=";Wu*AL4mu42380:GET DIGITSu>A$" "ĺUA;:2130uHUA(A$)uRS$"U"L0ī2020u\S$" "S$","ī2300ufL0ī2020up","18)"L=";uzAL2v2380:GET DIGITSARAMETERS tlLOL:MOM(tv".":"E=";:tS$"X"Č7139CtAL6Yt2380:GET DIGITSotA$" "ĺE;:1970{tE(A$)tE158ĺ" >157";:1910tS$" "S$","ī2290tL0ī2080t","10)"U'=";t2090t","18)"U=";tAL3 u238s$s&S$"X"ĺ32)"U*U";:1870Bs0Y0ĺ","31)"TOP";:1870ds:YYMĺ","31)"BOTTOM";:1870xsD","31)"SIDE";sN5:0,YMEXM,YMEsXA$""ĺ".":" ADJUST ENERGY E FOR CLOSEST APPROACH":" OF WAVE TO X AXIS ON THE RIGHT"; tb------------PM5)'rDUDU(V(0)1.75LLE)UOMD23rUUODUArX1XM1brDUDU(V(X)LL(XX)E)UMDmrUUDUwrXX1rYYMEUrS$"X"YYMEUUU1r(YYC)YCī1830rKEEV(X)LL(XX)r28X(1(KE))2,YrDUDUKEUMDsUUDU'=2, U=0, M=5";:E107.5:UA2:1610Uq@"E=49.2, U'=0, U=20, M=5";:E49.2:UO20pqJ---------------PLOT UqT5:0,YMEXM,YMEq^3qhYME8ī1670qrL0Ĕ88276,YME2q|L0Ĕ82276,YME2qMDM100000rDUUA(3MD)(L2)(1(L)pVOV(0)1.75LL7p(VOYC)YCVOYC(1(VOYC))?pX1Ip5312fpS$""(L0LO0)ī1610p---------------SAMPLESp""SAMPLE VALUES OF PARAMETERS:"p,L0ĺ"E=89.2, UA=1, L="L", M="M;:E89.2:UA1:UO0:1610%q6W$"3"ĺ"E=107.5, UooVV(X)*oV0V159ēX,158V0oPoL0:M5:XM279:YC79:YM158eoV(0)2V(1)V(2)o--------------PLOT V(X)o(L)LOĺ".":" THIS INCLUDES 'CENTRIFUGAL POTENTIAL'.":" U IS A RADIAL AMPLITUDE (SEE TEXT)."oLL100000L(L1)Mвѭ2WW]2z1P222PVVW]*+%$*1,PVV\ЬЭѲѳ+*+%%$22VVVzW]ѭs**%%%**+P2\{Ь׳s++%*%%%$2VVz{]^s*++++,P]вѳ2WW]2z%$$%2VWWW{*++++,2WЭѭ2WW{2z1P222UVVz~*+$%$%+122VW]]ѲѲѳץm%**+$%%22VVVz\{O%**%%%%*122zѭײ++%*%%2VWV{]Э؀+%++++PVA$vW$(K);:1930,v --------------INFO2000tH-----------PARAMETERStR(A$)0A$" 0"A$" "t\5J1tfAM10ıtpJ2170,2190,2210,2230,2250,2270,2290uz sJ8ĺ:s5J1#sA$" "+sS$EsS$"-"A$"-":5J1[s(0)5J2ī2050usS$(8)JNJ1:2120sS$" "(S$"-"S$"9"S$"/")ĺA$" ";:5JsS$"."S$"9"S$"/"(A$)5A$A$S$:S$;s ((A$))AMS$(8)tS$3PG:PG16301,0:ST$"S"ī1840+rDST$A$frNA$(27)ĉ::28)"T="100T310T2T1".":990:M,V,R,rXA$"E"ī1350:GRIDSrl40:CALCULATErv----------GET DIGITSrJN1rJJNrJ0K4ġ:1080rJ0Ģ24::860sS$(27)Ģ24::750q9038,182Aq15,15318,15718,16119,16119,15722,153:"Y"Pq140:PLOTkq--------------DRAW A$zqM1(A$)q((A$,M,1))X,YqXX7qqq--------------KEYPRESSq(16384)128ľA$:ST$A$q0ST$"S"ľA$ r:A$"X"PGA$"M3 "M$(4)p@X219:Y191)pJ1760?pT7135:P.1 TO P.2Np^8938,182tph15,15321,15315,16121,161:"Z"p|230,64:16299,0:PG2pA$"T= "(T1)pX157:Y191p1760pT30ĔT348171,191:T248178,191pT20ĔT248178,191 ,161:12,1536,161:"X"7oA$"FOR X PLANE, PRESS X."EoX3:Y182Oo1760loA$"FOR SINGLE STEP: S."zoX3:Y191o1760oA$"M1 100"oX219:Y173o1760oA$"M2 "M$(N)oX219:Y182o1760o"N2ī1620o,0236,188p6p 9,179:A5z A$"@CONSTANT AND F IS FREQUENCY."C 9,189:AQ 16368,0Y A$t 16300,0:230,32:360A9:Az A$"@CONSTANT AND F IS FREQUENCY." 9,189:A 16368,0ǃ A$σ 10AA$ރ 10m 146,138169,138E* A$"T@HE PROGRAM YIELDS @E@ = 10, 30, 50,...,"S4 9,159:Ao> 78140,162:78141,162H A$"@SO WE GET THE WELL-KNOWN @E@ = 1/2, 3/2,"R 9,169:A͂\ 14186,171:14187,171f A$"@5/2,..., TIMES HF, WHERE H IS @P@LANCK'S".01" 9,123:A, 1452,125:1453,125H 78158,126:78159,126i A$"@AND @M@ = 5; WE OBTAIN"w 9,133:A A$"E = (E@ /20 (]^K/M)." 8,44:9,146:A4Ɓ 1451,148:1452,148 41120,146:41121,146 7893,149:7894,149A$"@AND MODEL ONES ON THE RIGHT."/l 9,90:A`v A$" E@XAMPLE: IN THE HARMONIC OSCILLATOR,"n 9,102:A A$"@WHERE @E = V@(X) = KX@^@/2, WE SUBSTITUTE" 9,112:Aˀ 1453,114:1454,114 A$"@X@^ = 2E@ /K AND @X^@ = 2@E /K, @WITH @K = @P@LANCK'S CONSTANT OVER"& 9,44:AC A$"2]. S@O WE MAY SET"P 9,54:Av A$"@M@E@ (X/])@^ = ME X^/200000"& 8,30:9,68:A40 1446,70:1447,70: 78134,71:78135,71N A$"@WITH REAL-WORLD QUANTITIES ON THE LEFT"X 9,80:A"b OF UNITS."'~ 8,35:9,10:A6981:A4^~ A$"T@HE QUANTITY M@E@ (X/])@^@ IS DIMENSIONLESS;"k~ 9,24:Az~ 14107,26~ 14108,26~ A$"@HERE M IS MASS, @E@ ENERGY OF NTH LEVEL,"~ 9,34:A~ 14123,36:14124,36 A$"@X POSITION, AND ] BILITY"} 9,160:AE}" A$"@OF FINDING THE PARTICLE AT RADIUS @R."S}, 9,170:A}6 A$" T@O ADJUST MASS, PRESS @M@ (DEFAULT 5)."}@ 9,182:A}J 16368,0}T A$}^ 16300,0:230,32:360}h ----------------PAGE 5}r :3 ~| A$"5: DISCUSSIONELS"| 9,120:A@| A$"@OF A SPIN-FREE HYDROGEN ATOM CAN BE"N| 9,130:A| A$"@FOUND. @P@RESS @L@ AND ENTER ANGULAR MOMEN-"| 9,140:A| A$"@TUM IN UNITS OF @P@LANCK'S CONSTANT OVER"| 9,150:A} A$"2]. U^ @BECOMES THE RELATIVE PROBAA SINGLE PEAK; AN INTERMEDIATE",i9,92:A\iA$"@FREQUENCY GIVES A SHORTER, WIDER PEAK"ji9,102:AiA$"@WITH THE SAME TOTAL AREA."i9,112:AiA$" F@OR AMPLITUDES, PRESS @A."i9,124:AiA$" T@O CONNECT THE DOTS, PRESS @C." jRA$"@NEL 1, 0 TO 5 VOLTS) 140 TIMES IN 1/60";h\9,50:AohfA$"@SECOND. @I@T THEN FREQUENCY-ANALYZES THE"|hp9,60:AhzA$"@DATA IN ABOUT 1/3 SECOND."h9,70:AhA$" A @FREQUENCY WHICH IS A MULTIPLE OF 60"h9,82:AiA$"H@Z YIELDS OMPUTER EXPECTS AN EIGHT-BIT 100-"6g 9,10:A6981:AhgA$"@MICROSECOND ANALOG-TO-DIGITAL CONVERTER"ug 9,20:Ag*A$"@IN SLOT 3. @I@T READS HEX @C0B0 (M@OUNTAIN"g49,30:Ag>A$"@CHANNEL 0, -5 TO 5 VOLTS; @J@OHN @B@ELL CHAN-"gH9,40:A.h 50 THEN Y = 50" fX" RUN 640"&fb5flUSER WAVE;fvKf1520:GRIDXfX0139af620rfY127Y127fY0Y0f2X,Yf6144X,Y:$1800ff7,128f4208:$1070f5f--------------A/Df:16302,0"gA$" T@HE Ce:5e"PROGRAM YOUR WAVE ON LINES 621-629.":Se"THEN TYPE 'RUN 640'.":e&"HORIZONTAL COORDINATE X, RANGE 0-139.":e0"VERTICAL COORDINATE Y, RANGE 0-127.":e:"EXAMPLE:":eD"621 Y = 50 - 50 * COS(6.28* 4 * X/140)"fN"622 IF Y >4096:$1000$d|-------------INPUT4d95180,184@dN115Xd(16384)128ī440^dgd380odA$dA$(27)Ĺ104,12:10dA$"?"A$(13)A$"2"dA$"1"ī1190dA$"2"ī750dA$"3"ī510dN(0):380e--------------YOU9,134:A-cA$" C@HOOSE SOURCE OF WAVE:";c9,147:A_c"A$"1. E@XAMPLE (SQUARE WAVE);"mc,9,159:Ac6A$"2. A/D @CONVERTER;"c@9,171:AcJA$"3. Y@OU CONSTRUCT A WAVE."cT9,183:Ac^(4096)169ĺ(4)"BLOAD BFREQ"ch16368,0 dr BE 1/60"b9,90:AIbA$"@SECOND, AND SO FREQUENCIES ARE MULTIPLES"Wb9,100:AbA$"@OF 60 @H@Z, UP TO A MAXIMUM OF 4140 @H@Z."b9,110:AbA$" T@O GO BACK OR ESCAPE, PRESS @ESC."b9,122:AbA$" T@O PROCEED, PRESS @RETURN." cITUDES OF THE FREQUENCY COMPON-"-ad9,48:A`anA$"@ENTS OF A COMPLEX WAVE FORM. (@T@HEY ARE"max9,58:AaA$"@PROPORTIONAL TO INTENSITY AND ENERGY OF"a9,68:AaA$"@THE WAVE COMPONENTS.)"a9,78:A bA$" T@IME INTERVAL IS ASSUMED TO`(104)96Č506881` --------------INTRO:`:3g`A$"F R E Q U E N C Y A N A L Y Z E R"`(8,16:A6981:9,10:A4`2A$"R H G@OOD 1984"`<8,90:9,24:A4`FA$" T@HIS PROGRAM DISPLAYS THE SQUARES OF"`P9,38:A aZA$"@THE AMPL     560:INTROM68,0{ A$/{ 560:INTRO0."zZ 9,167:AEzd A$" S@TABILITY OF ORBITS: USING DEFAULT TWO-"Szn 9,179:Azx A$"@BODY PARAMETERS, TRY @P@ = -2.9 AND -3."z 9,189:Az 16368,0z A$z 560:INTRO:2.9 AND -3."& 9,189:A& 16368,0& A$' 560:INTROOON, IN THE DEFAULT""y 9,125:AWy A$"@3-BODY MODE, FOR @M@3 SET @X = 83, Z = 10."ey 9,135:Ay( A$" F@OR A @T@ROJAN ASTEROID (@L@AGRANGE POINT):"y2 9,147:Ay< A$"M2: 1 86 50 0 -5 8.6 0"yF 9,157:AzP A$"M3: 0 86 -50 10 5 8.6 EFAULT 3-BODY PARAMETERS YIELD A".x 9,83:A`x A$"@CIRCULAR ORBIT (2@]X = VT). T@O ADJUST"mx 9,93:Ax A$"@THE @Y@ SCALE, PRESS RESET, THEN @LIST 410,"x 9,103:Ax A$"@ADJUST, AND TYPE @RUN."x 9,113:Ay A$" F@OR A @U@RANUS-TYPE MV A$"@THAT THE CENTER OF MASS, +, OF THE"7w` 9,39:Ahwj A$"@SYSTEM IS AT THE CENTER OF THE SCREEN."uwt 9,49:Aw~ A$" T@O DISPLAY @K@EPLER'S LAWS, FIRST SET"w 9,61:Aw A$"N@=2 BODIES, @M2=0, Z@=0, AND @VZ=0."w 9,71:A!x A$" T@HE D---PLAYch4096:$1000(cr104,12:1049,129b4544,b-----------RACHMANINOFF]b4208,96:4211,165:4353,150:4377,21:70,24zb198,200,204,187,136,149bN15bI:251,Ib"4211:$1073b,b64353,0:4377,30b@I:251,IbJ4211bT4208,173:4211,16c^------------ CORRESPONDS"ad9,56:A4anA$"@TO THE NOTE @C."Aax9,66:AdaA$" T@O ESCAPE, PRESS @ESC."qa9,78:Aa(4)"BLOAD BMUSIC"aN0164a0,116N279,116Na0,164N279,164Naa8,0:69,177:70,5:71,0a4544:$11C0b6)`(104)96Č506886` ------------------INTRO ?`:3R`A$"M U S I C"n`(8,95:9,20:A6981:A4`2A$"R H G@OOD 1984"`<8,82:9,34:A4`FA$" T@HE KEYBOARD CORRESPONDS TO THE PIANO"`P9,46:A aZA$"@KEYBOARD, AND THE LETTER @S@    ql16368,0qvA$$q20:INTRO."p9,116:AGpA$"P@RESS @K@ TO KEEP IT. @S@UCH PROPERTIES ARE"Up&9,126:Aop0A$"@EVEN CLEARER IN"}p:9,136:ApDA$" @20 COS(8X) + 40 COS(10X) + 20 COS(12X)."pN9,147:ApXA$"P@RESS @X@ TO COMPARE WITH THE PRECEDING."pb9,158:A(-1) @COS(NX)."o9,84:ARo53,8452,8545,8548,8149,8146,7752,7853,78jo1488,80:1489,80oA$" A@ WAVE HAVING SOME PROPERTIES OF A"o9,96:AoA$"@WAVE GROUP IS OBTAINED WITH"o9,106:ApA$"@ - 40 COS(9X) - 40 COS(11X)ITH"nh9,42:ADnrA$"@100 SIN(NX)/N = 100 SIN(X) + 50 SIN(2X)"Qn|9,52:An31,5230,5323,5326,4927,4924,4530,4631,46nA$"@+ 33 SIN(3X) + ..."n8,115:9,62:A4nA$" A@ DELTA-FUNCTION IS GIVEN BY"n9,74:AoA$" 10 -------INFOm:16302,0:3Pm"A$" T@HE SQUARE WAVE CONVERGES MORE SLOWLY"dm,9,10:A6981:Am6A$"@THAN THE TRIANGULAR ONE AND SHOWS THE"m@9,20:AmJA$"G@IBBS OVERSHOOT AT THE CORNERS."mT9,30:An^A$" A@ SAWTOOTH MAY BE OBTAINED Wlx------------------GRID'l:2Hl0,00,158272,158272,00,0Yl0,79272,79hl0,396,39yl0,1196,119l266,39272,39l266,119272,119lX6820468lX,0X,6lX,76X,82lX,152X,158ll3l m--------(A$)1ĺ(8)" 0";:%kA(A$).4=k16304,0:GRAPHICSHkT$"G"dk------------------PLOT}k S$"S"İ1400:GRIDk0,YCkX0Lk(FF(X)AS(P)k2F(X)Fk<(F)YCF(F)YCkFXX,YCFkPPPNkZPLPPL(PL)kdlnA$;.jS$"0"S$"9"(A$)4A$A$S$:S$;Hj((A$))100S$(8)njS$(8)ĺS$" "S$;:(A$)1ī1050jS$(8)A$(A$,(A$)1)jS$(27)ġ:20jS$"T"T$"T"Ĺ16304,0:T$"G":1070jS$"T"ĉ:T$"T"jS$(13)S$"S"ī1070ki.S$0i8S$"X"Ĺ16299,0:S$:16300,0:1070[iBS$"K"ĺ"K";:7132:(8);:1070:KEEPliLA$""ī1160iVS$(8)ĺ" 0";:NN(N)(P)::970i`S$"0"S$"S"S$(13)S$(21)ĺ" 0";:ijS$" "(S$"0"S$"9")A$" "itS$"-"A$"-"j~SS BACKSPACE. "Dh"TO REVIEW PREVIOUS VALUES, PRESS T";kh".":"HARMONIC #"N","15)"SINE:";shP0h1050:GET DIGITSh";"27)"COSINE:";hP34h1050:GET DIGITShN40NN1h970h------------GET DIGITSh$A$""2 gHP0gRS$6g\S$"K"ĺ"K";:7132:(8);:KEEPHgfS$(27)ī20lgpS$"X"Ĺ16299,0:S$:16300,0gzS$"S"S$(13)ī680g850g-----------3:CONSTRUCTg1400:GRIDg"INPUT RELATIVE AMPLITUDES, -100 TO 100."h"TO GO BACK, PRE---------2:TRIANGULAR=f"TRIANGULAR WAVE, "(N1)2" TERM";[fA50(1)((N1)2)(NN)xf---------------BOTH 1,2f N1ĺ"S";f"."f 1280:PLOTf*:"TO DISPLAY NEXT PLOT, PRESS RETURN."f4"TO SUPERPOSE NEXT PLOT, PRESS S. ";g>NN6384)128ī620eXeb570%elM$?eM$(27)Ĺ104,12:10WeM$"?"ī1550:INFOleM$(13)M$"1"eM$"1"M$"3"ī550e:21e(M$)700,740,910e--------------1:SQUAREe"SQUARE WAVE, "(N1)2" TERM";eA60Ne770f-0dK0ī520dK3.14683dF(136):FUNCTIONFdS(135):SINE RdX134_dS(KX)jdS(X)SxdS(68X)SdS(68X)SdS(LX)Sdd550dX0LdF(X)0dd&X(16336)(16336)d:95242,172dDX120eN(1IANGULAR WAVE;"c"9,158:AIc,A$"@ 3: YOU CONSTRUCT A WAVE."Wc69,172:Arc@-----------------INITcJP0:PHASE cTF0:FUNCTIONc^X0:ABSCISSAchYC79:Y-CENTERcrL136:LENGTH c|A0:AMPLITUDEcN1:NUMBER d16368,9,94:A8bA$" T@O SEE THE PICTURE KEPT, PRESS @X."Fb9,106:AtbA$" T@O GO BACK OR ESCAPE, PRESS @ESC."b9,118:AbA$" T@O PROCEED, PRESS @RETURN."b9,130:AbA$"C@HOOSE 1: SQUARE WAVE;"b9,144:AcA$"@ 2: TRdA$"@MONICS OF GIVEN AMPLITUDES. @A@RBITRARY"=an9,50:AjaxA$"@WAVE FORMS MAY THUS BE CREATED AND"wa9,60:AaA$"@COMPARED."a9,70:AaA$" F@OR FURTHER INFORMATION, PRESS ?."a9,82:AaA$" T@O KEEP A PICTURE, PRESS @K." b%`(104)96Č50688` 9`----------------INTROL`:16302,0:3|`(A$" F O U R I E R S Y N T H E S I Z E R"`29,12:A6981:A`<A$"R H G@OOD 1983"`F8,77:9,26:A4`PA$" T@HIS PROGRAM ADDS SINE AND COSINE HAR-"`Z9,40:A0a            m  ɕ`JJJJ)0 ' # * 8      p Й Е  q`   ((((((((((((((((((((((((((((((((PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP                         !""##$$%%%&&&&&&&&&&&&&%%%$$##""! 0I`'@&'&  *  Lii    s  K  # `$;73/+'#` UT 0e) '@&0 @&&&&i)i(e '@&0 @&&&& i('@&0 @&&&&00L ee)i),ɛ`ɰ0ɺ)  0  L  " (S@CREEN SIZE: 128X80.)":9,191:A6lP,0:A$:20,8,0:A$!k8A$(13)ī420:GRAPH4kB16299,0:380$REFERENCE FRAME)." j9,116:AQjA$" W@HEN K = 2, THE TWO WAVE SPEEDS ARE"_j9,128:Ayj4960,130:4961,130jA$"@EQUAL, AND THE WAVE PATTERN APPEARS"j9,138:AjA$"@'FROZEN' AS IT MOVES ACROSS THE SCREEN."j$9,148:Ak.1636,74:Ai7190,76:7191,76KiA$"@AND THE GROUPS GO TOWARD THE LEFT."Xi9,84:AiA$" W@HEN K = 4, THE TWO WAVELENGTHS ARE"i9,96:Ai4960,98:4961,98iA$"@EQUAL, RESULTING IN STANDING WAVES (IN A"i9,106:AjA$"@MOVING $"@SUM IS U = (W -W )/(K -K ).".h*9,52:AAh4A$"1 2 1"Wh>8,125:9,54:A4mhH759,54:760,54hR50102,54:50103,54h\A$" I@F THE WAVE LENGTH INCREASES WHEN THE"hf9,64:AhpA$"@FREQUENCY INCREASES, THEN U IS NEGATIVE"iz9E 1 IS U = W /K ,"g9,9:A2gA$"1 1 1"Hg8,185:9,11:A4{gA$"@WHERE W IS @2]@ TIMES FREQUENCY AND K IS"g9,20:AgA$"2] @DIVIDED BY WAVELENGTH."g9,30:Ag A$" T@HE GROUP VELOCITY CORRESPONDING TO THE"g9,42:A!h A50263,59:50264,59$fNA$"@K =4":fX8,255:9,69:A4Tfb50262,71:50263,71bflA$" SUM"yfv8,252:9,122:A4f7135:P1 TO P2f6,5:7,1:8,33f4096:$1000f10f----------------INFOf:16302,0gA$" T@HE SPEED OF WAVA$" S @SINGLE STEP @ESC@ ESCAPE":e9,189:AIeA$"@W =1"_e8,254:9,16:A4ye49263,18:49264,18eA$"@K =5"e8,255:9,28:A4e49262,30:49263,30e&23256,57:23257,57e061270,57e:50276,57:50277,57fDh9,180:A6656,1:6672,0:6688,20:6704,0ehH4096mhRA$uh\20hf---------------SUBhpA$" C@HOOSE:"hz9,150:AhA$(1)"1. S@OUND, MOVING SOURCE."hA$(2)"2. S@OUND, MOVING OBSERVER."i$"@V/C ="!g8,210:9,189:A41gX250:Y189@gM1(V$)SgN((V$,M,1))ggNX,Y:NX1,YqgXX7wggA$"D@ETECTOR"g8,119:9,172:A4g27143,161g7135gV2(V$)g 141,(V)g140,255(V(V))g 8,0:9,0"h*0%f0(V2$)201,150:(V2$)202,150.f:V3$AfDV3$(27)ī20XfNV3$(13)V3$"0"fXV3$(8)Ē0:(V2$)201,150:(V2$)202,150:3:490fbV3$"0"V3$"9"ī570fl(V3$)208,150:(V3$)209,150fvV$V1$V2$V3$f-------------GRAPH gA$e(V1$)194,150:(V1$)195,150-eV2$@eV2$(27)ī20_eV2$(13)V1$"."V$V1$seV2$(13)ī640eV2$(8)Ē0:(V1$)194,150:(V1$)195,150:3:430e(V2$"."V1$".")(V2$"."V1$".")ī490f&V2$"."(V2$"0"V2$"9")ī49" S@ET RELATIVE SPEED: V/C ="-d9,149:Agd(6)3A$"@(MUST BE LESS THAN 1)":8,40:9,158:A4tdV$".50"dV3$"":DP0d16368,0d(6)3V1$".":480dV1$dV1$(27)ī20dV1$(13)ī640eV1$"."(V1$"1"V1$"9")ī440A c870an9,47:ApaxA$"@FREQUENCY OBSERVED MAY DIFFER FROM THAT"}a9,57:AaA$"@OF THE SOURCE."a9,67:AaA$" I@F THE SPEED V OF THE SOURCE EXCEEDS"a9,79:AbA$"@THE WAVE SPEED C, A So`(104)96Č50688,` A$"A":YX112:E`--------------INTROX`:16302,0:3}`(A$"D O P P L E R E F F E C T"`28,33:9,9:A6981:A4`<A$"R H G@OOD 1984"`F8,76:9,23:A4`PA$" W@HEN A CONSTANT-FREQUENCY WAVE SOURCE"aZ9,3          A$"@THE CELL FARTHEST LEFT DISAPPEARS. @T@HE":9,104:AYbxA$"@RESULT IS:":9,114:Ab27105,116:27110,116:27110,112:27105,120bA$"S@UBSEQUENT GENERATIONS PRODUCE":9,134:AbY1271354:27220,Y:27225,Y:cA$"@AND FINALLY S BORN IN A":9,46:ADaFA$"@SPACE WITH THREE NEIGHBORS.":9,56:AaP27100,68:27105,68:27110,68:27110,64:105,71106,71aZA$" F@OR EXAMPLE, IN THIS CASE, IN THE NEXT":9,84:AadA$"@GENERATION A CELL APPEARS AT THE DOT, AND":9,94:A:bn7 `(104)96Č50688/` (4)"BLOAD BLIFE"K`4121,13:4106::::3s`A$"L I F E":8,98:9,8:A6981:A4`(A$"R H G@OOD 1983":8,77:9,22:A4`2A$" R@ULES: A CELL SURVIVES IF IT HAS TWO OR":9,36:Aa<A$"@THREE NEIGHBORS; A NEW CELL I  !"##$%%&'(()*+,,-./011234567789:;<;:987765432110/.-,,+*)(('&%%$##"!  159= @MT_is~@MT_is~@MT_is~@MT_is~@MT_is~@MT_is~@MT_is~@MT_is~@MT_is~@MT_is~ $(,048< $(,048"&*.26:>#'+/37;?#'+/37;? $(,048< $(,048"&*.26:>#'+/37;?#'+/37;? $(,048< $(,048156,161163,1619hH0157,159:0158,157:0159,155ShR0160,157:0161,159|h\A$"S@ELECT ATOMS BY SIZE OR SPEED."hf9,175:AhpA$"E@SCAPE: @ESC. D@OOR: ANY OTHER KEY."hz9,189:AhB$"1"Ĺ251,32:252,14iB$"2"Ĺ251,14:252,220,180g8,65:A4FgA$"C@HOOSE: 1. MIXED (MAXIMUM ENTROPY);"Tg9,154:AwgA$"@2. LARGE ATOMS ON RIGHT;"g8,65:9,166:A4g3g A$"T@EMPERATURE"g9,147:Ag 8,150:A4g*A$"R@EDUCTION OF ENTROPY: @S = -"g49,161:AATOMS ON RIGHT;"&f:8,65:9,166:A4FfDA$"@3. ALL ATOMS ON LEFT."\fN8,65:9,178:A4jfX16368,0zfb95220,180flI115fv(16384)128ī660ff610fB$fB$(27)ī370fB$(13)B$"1"fB$"1"B$"3"ī600g0:952,0-e2:0,150,137256,137256,150,15:3Pe128,15128,60:128,92128,137re127,61127,91:129,61129,91eA$"M@ A X W E L L ' S @D@ E M O N"e8,28:9,9:A4eA$"C@HOOSE: 1. MIXED (MAXIMUM ENTROPY);"e&9,154:Af0A$"@2. LARGE 4)"BLOAD BDEMON".dhCLICK(16336)(16336)Ndr16368,0:230,64:16299,0^d|95196,176jdI115d(16384)128ī430dd380dA$dA$(27)Ĺ104,12:10dA$"?"ī960dA$(13)ī370d----------------INPUTe:1630 YOU MAY PLAY"c9,128:A=cA$"@THE DEMON'S ROLE HERE."Kc9,138:Avc"A$" F@OR MORE INFORMATION, PRESS ?."c,9,150:Ac6A$" T@O ESCAPE, PRESS @ESC."c@9,162:AcJA$" T@O PROCEED, PRESS @RETURN."cT9,174:Ad^(4096)162ĺ(IOLATING THE"b9,88:AKbA$"S@ECOND @L@AW BY INTRODUCING ORDER, AND"Xb9,98:AbA$"@REDUCING ENTROPY, WITHOUT A CORRESPOND-"b9,108:AbA$"@ING ENERGY EXPENDITURE. @U@NFORTUNATELY,"b9,118:AcA$"@NO SUCH DEMON EXISTS. @B@UTTENDENCY TOWARD DISORDER AND"*ad9,46:APanA$"@TOWARD UNIFORM TEMPERATURE."]ax9,56:AaA$" M@AXWELL PROPOSED A DEMON WHO WOULD"a9,68:AaA$"@SELECT ATOMS OF A PARTICULAR KIND, OR OF"a9,78:A bA$"@HIGHER KINETIC ENERGY, THUS V`(104)96Č506882` ---------------INTRO=`::3d`A$"M A X W E L L ' S D E M O N"`(A6981:8,27:9,8:A4`2A$"R H G@OOD 1985"`<8,77:9,22:A4`FA$" T@HE @S@ECOND @L@AW OF @T@HERMODYNAMICS"`P9,36:AaZA$"@IMPLIES A      2$'%'%'%'%'%g%g56666 <,<<,<,< -> >66;6<,,'%g-> 5o> >6;6'<><,,< 5%5%->w366>$$$,<,<,<,,566636$%?,%?'->?@@AABCCDDEFFGGHIIJJKLL $(,048< $(,048"&*.26:>#'+/37;?#'+/37;? $(,048< $(,048"&*.26:>#'+/37;?#'+/37;? $(,048< $(,048"&*.26:>#'+/37;?#'+/&`((((((((((((((((((((((((((((((((PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP !!!!!!!"""""""#######$$$$$$$%%%%%%%&&&&&&&''''''' 8$0'u ` ɝ8$0'8v `Ii )IiJJJ$`&@'0  Q&&@ pQ&&`Q&&Q&` G8Ii8EIGE 03$I0HhIHh`$I0< 8pE FG  F0I` 8pE FG  F`GeE88Epɀ `ɡhh` Ȅ$ 렘1  0  `  0  ` pG G ^8IiE$ $G?hh G   @G @ G G @'&1&@Q&&ȩ1&Q&& $   1&@Q&&ȩ1&Q&&  L`L1&09Q&&@1&@(pQ&&ȩ1&`Q&&ȩ1&Q&&L @'& @Q&&Q&& $  ` ` @Q&&Q&&L0  Q&&@ pQ&&`Q&&Q&&L eFߐIieGɭIiɛ`$J䠀 W @ L`FG }P FFI}P FFI}P FFI}P GGI}P GGI}P GGIFGL~L @HLP 0`"&*.26:>#'+/37;?#'+/37;? $(,048< $(,048"&*.26:>#'+/37;?#'+/37;? $(,048< $(,048"&*.26:>#'+/37;?#'+/((((((((((((((((((((((((((((((((PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP  }Zɛu @L - 橿 < FUTЪɛ0  䩿%L` ޠL WF  :F`IIiIIiJfFf;0700y0*$P(JJ8Je8Ii Gʽ&@'0 @&&ȩ&&ڽ&@'0I0 ?1&&ȩ~1&&萺0 0  FLL&F Jiq' ) L-'G0fD0 &eFmFe&H&IieF"FIie&Iie'e ɕ #'#L-LФ`0 FE88jyJPe٥&*##&0#"8PyP8yP8PѩЅ0L&r'ݠFGF}pFGiG&FG8FpFGG&0'`(3>IT_it~E$LL 0i&@'0  000I1&&&@'0&&AfA$"@TYPE @Y."#f9,126:A1f16368,0@f9560,128LfN115df(16384)128ī790jfsf 740{fA$f A$(27)ĉ:f*A$"Y"Ĕ8960,126:104,12:3072,0::(4)"RUN MENU"f4:670AGUAGE SUBROUTINES. @T@HEY"(el9,72:AWevA$"@DO NOT STAND ALONE; BUT THE DISK MAY"de9,82:AeA$"@BE COPIED WITH @COPYA.)"e9,92:AeA$" T@O ESCAPE, PRESS @ESC."e9,104:AeA$" S@ET @CAPS LOCK@ IF YOU HAVE IT, AND"f9,116:dA$"@DEMONSTRATION AND SUPPLEMENTARY STUDY";d9,30:Ald&A$"@AT VARIOUS LEVELS, IN CONJUNCTION WITH"yd09,40:Ad:A$"@APPROPRIATE LECTURES AND TEXTS."dD9,50:AdNA$" (T@HEY ARE WRITTEN IN @BASIC@ WITH"dX9,62:AebA$"@MACHINE-LAN1XX4cLC0cN1(A$)2cA((A$,N,1))JcA64LC64LC:470_cA77A87XX2pcA64AALCcAX,Y0:AX1,Y0cXXDXccc----------------INFOccA$" T@HESE PROGRAMS ARE FOR CLASSROOM"c9,20:A6981:A."C@ALIFORNIA @S@TATE @U@NIVERSITY, @H@AYWARD"?bX0132:Y0156Hb310YbA$" 1986"jbX041:Y0168sb310b"PAUSE02000:b,490b6----------------DRAW A$b@0bJYY09Y03bT139X0,Y139X0,Yb^bh3brX149X0c|Y06DRAW A$, POKE 9,Y:CALL 6981 (A$ IS FIRST VARIABLE)>an::Qax28,146:62454oaA$"INTERMEDIATE PHYSICS"aX097:Y049:DX9a310aA$" SIMULATIONS"aX097:Y061a310aDX7aA$"R. H. G@OOD"aX041:Y0144a310-bA$)` 232,0:233,28:SHAPE TABLE ADDRESS6`1:0:3^`10,76:11,29:12,27:USR(X)=SQR(X)u`((4)"BLOAD BFILE"`2BSAVE BFILE,A$1B00,L$500`<TEXT P1 TO P2, CALL 7139`FHI-RES P1 TO P2, CALL 7135`PBOTH, CALL 7132`ZONERR, CALL 71264ad     A12XX2elAX1,Y#evXXDX)e2eDX78e?e0Ze--------------CHARSETieX42:Y105ueN095eNX,Y:NX1,YeXX9:X140X42:YY10ee16368,0e768e104,12:10(,W@HITE,203,56,O@RANGE,201,74,B@LUE,201,92,S@CREEN,201,156,@SYNC,215,166,@CHECK,208,176ld9,44,70,5,44,63udDX8dN115dN13Ę48dA$,X,Yd&LC0d0M1(A$)d:A((A$,M,1))dDA64LC64:640dNA64AALCdXAX,Y ebA952,V272,Vccc02c252,123272,123Gc252,142272,142\c252,161272,161cc3~c--------------STRINGScSCREEN TEST,47,14, R H G@OOD 1984,41,30 ,105,80, 92,T@HIS SHOULD,58, 64,@BE SQUARE.,61,74WdG@REEN,201,20,P@URPLE,201,38----------BANDS bVO108719*bCC17bC4C5>bCNbVVOVO17_b252,V272,Vebkbrb5b"H2532712b,H,105H,179b6b@VO10614438bJ1bTVVOVO162b^252,V272,Vbhbr2b|VVO19VO352 c2,145,38,32,4,245,202,208,244,96.a(P768835:a2Q:P,Q@a<WaF------------LINES]aPdaZ3tadV019095an0,V279,V279,V10,V1axa 0,34,139,244,278aI15aHaH,0H,191H1,191H1,0aa7:0,191279,191b-`(104)96Č506880` --------------SYNC`162,252,160,0,32,36,3,162,3,32,34,3,162,10,32,34,3,169,58,32,168,252,169,255,205,222,192,240,227,174,0,192,16,246a160,1,169,143,32,17,244,169,128,32,51,3,32,4,245,169,255,133,69,162,18,165,69,81,3837;?M%@j@@6e$$ -o$,- ,-5o%<#$d-5 $$$36-6o$$< $$$M-'$$4 $$$666$$$$$$$$ -667. $$$-?$$$?M5#$JMb$$4 $$36v $$2$$4  v.$d v-' +@MT_is~'4<IP_|lx.<o%$?N:'$$)6o%$$;6-%?6 #$, $ -56) `L !Ji@H 멓 f꩘ ƝhJ`iȱi"`\MW @勅20   ƈ iП   Lʚ` @GJ'F&&F'G     :A7iA$"@OF THE VERTICAL DISTANCES FROM THE POINTS"Ei9,121:AxiA$"@TO THE LINE, IN TERMS OF THE CORRESPOND-"i9,131:AiA$"@ING EXPERIMENTAL ERRORS @SD."i9,141:AiA$" F@OR MORE INFORMATION, PRESS ?."i9,153:A)jA$" F@O\9,67:A=hfA$" W@E ASSUME THAT THERE IS NO ERROR IN @X"Jhp9,79:A~hzA$"@AND THAT @Y@ VALUES ARE NORMALLY DISTRIB-"h9,89:AhA$"@UTED WITH STANDARD DEVIATION @SD."h9,99:AhA$" C@HI-SQUARE IS THE SUM OF THE SQUARES"i9,111OGRAM PLOTS YOUR DATA AND LETS",g 9,37:A`gA$"@YOU DO A LEAST SQUARES FIT, BY MINIMIZING"mg 9,47:Ag*A$"@CHI-SQUARE ( @^@), USING THE GAME PADDLES"g49,57:Ag>81,5283,5286,5888,58gH81,5887,5288,52gRA$"@OR THE KEYBOARD." hX(40):Y(40):S(40)&fP0100:P11206f6,P1:7,P0BfM0:B0SfCH0:CM9999of-----------------INTROwf:f:3:A6981fA$" L E A S T S Q U A R E S F I T"f9,9:AfA$"R H G@OOD 1983"f8,80:9,23:A4gA$" T@HIS PR3,8,80,23,32,211,244,201,32,208,4,165,38,240,25,165,48,81,38,145,38,165,8,73,128,133,8,6,48,16,212,169,1,133,48,200,192,39,208,205,96:XLINEe:I768832eDD:I,DeNeX480eb .1,.5,1,5,10,50,100,500,1000,5000elI110evA(I)efTHEORETICAL= ";d802d----------------ONERR=d(7);Sd(218)200ī1430hd(218)24ī1510~d(218)164ī1640dd------------------INITd&A$"A"e0165,7,162,29,160,0,132,8,32,17,244,165,48,81,38,145,38,165,6,73,128,24,101,8,13:410Pc|PK216ĺ:(7):" WON'T DO LOG PLOT; DATA GO BELOW 0.1. ";:A$:PK155jcPK155ĉ:2060:LIST{cPK141ī40c-----------------THEOR.c768:XLINEc2900:THPLOTcMMTH:BBTHcX$"X"Ģ22:1:"Y = MX + B";:170d21:23:"0)2:P1((1)P1)2$bPK(16384)4bPK128ī30Qb"---------------KEYPRESS_b,16368,0qb6KP$"P"ī370b@PK201P03P0P0DPbJPK202P12P1P1DPbTPK203P1253P1P1DPb^PK205P0189P0P0DPbhDP3crPK216YL.1X$"X""Y";"a" = "(MRM.5)RM" X ";8aBRB.50ĺ"+";Sa(BRB.5)RB";"23);paX$"X"ĺ41):3010:LOGxa34aCHCMĺ"> 9999";:250aCH99CH(CH)a"= "(CH10.5)10" ";aCHCBCBCH:21:150bKP$"P"P0(191(0).745P$`(104)96Č50688'` 540:INITD`-------------------LOOPM`DP1i`(M(128P1)YM(74.5XM)`2B(150P0)YM142`<768`F6,P1:7,P0`P768:XLINE`ZCH0`dI1N`nD(Y(I)MX(I)B)S(I)`xCHCHDD``22`1a  68,0230,32:62450N$CN$"A"N$"G"N$((N$)55)U"N$(27)ĉ:a,N(N$)t6N1N16ī270@A$A$(N)J9,11N43(N10):AT16300,0^104,96:24576,0:4096,0h:(4)"RUNG"N$AEQUENCY @A@NALYZER"=A$(12)" C. L@EAST @S@QUARES @F@IT"gA$(13)" D. R@ELATIVISTIC @M@OTION"A$(14)" E. L@IFE"A$(15)" F. M@USIC"A$(16)" G. S@CREEN @T@EST"N116A$A$(N)9,11N43(N10):A163ND @P@ARTICLE"8 dA$(5)" 5. T@HREE @B@ODIES IN 3-@D"O nA$(6)" 6. G@AS"t xA$(7)" 7. M@AXWELL'S @D@EMON" A$(8)" 8. D@OPPLER @E@FFECT" A$(9)" 9. S@UM OF @T@WO @W@AVES" A$(10)" A. F@OURIER @S@YNTHESIZER"A$(11)" B. F@R0 (233)28(104)12(6941)165Č50688; :3:G A$(16)i (A$" T@O ESCAPE, PRESS @ESC."~ 2A6981:9,189:A <A$(1)" 1. R@ADIATING @D@IPOLE" FA$(2)" 2. M@OVING @C@HARGE" PA$(3)" 3. F@REE @P@ARTICLE" ZA$(4)" 4. B@OU   23)"CHI-SQUARE "s41)Ls"FOR THEORETICAL LINE, PRESS RETURN KEY.";Zs16368,0hs20:LOOPs ----------------LISTss N1ī1590:INPUTs*2180:TICKSs42550: AXES s>I1NsHXX(I):YY(I):SS(I) tR"INPUT X("I"),Y("I"),0#rv"ADJUST SLOPE M WITH PDL(1)"Sr"AND Y-INTERCEPT B WITH PDL(0). (RETURN)";]r1960r"ADJUST SLOPE M WITH KEYS J AND K"r"AND Y-INTERCEPT B WITH KEYS I AND M. ";r768rA$rA$(27)ī2060rr21:23)"BEST SO FAR= "s41)qKP$"K"KP$"P"ī1960:q&22:12)"KEYBOARD (K)"Wq010)"OR PADDLES (P)? ";jq:16368,0:KP$qDKP$(27)ĺ:2060:LISTqNKP$(13)KP$"K"qXKP$"K"KP$"P"ī1850qb:"THE EQUATION OF THE LINE IS Y = MX + B.":rlKP$"K"ī194Y,SDpX0XXMY0S0SY40YM142YS150YM142ĺ(7);:1640]pX(I)X:Y(I)Y:S(I)Smp2640:PLOT}pII1:NN1pN41ī1640p--------------PROCEEDp2780:CALCp1:41)p16304,0:GRAPHICSp35,24:TEXT WINDOWq24:ICKSo@2550:AXES,oJ--------------DATA8oTI1:N0Co^KP$""ioh"INPUT X("I"),Y("I"),SD("I"): ";wor16368,0o|(16384)128ī1660o(16384)155ī660:INITo(16384)196NN1:2060:LISTo(16384)141ī1760:PROCEEDp"";X,1440n"";XM/nXM1XM9999ĺ(7);:14305n\n"SPECIFY MAXIMUM Y, 1 TO 9999: ";jn16368,0n(16384)128ī1530n(16384)155ī700:INTROn(16384)141ī1520n"";YMn"YM1YM9999ĺ(7);:1510n,16304,0o62180:T:1330"mP57229,189:57230,1895mZPAUSE1500:;mdWmn-------------XM AND YMamx2550im21m"FOR YOUR DATA,"m"SPECIFY MAXIMUM X, 1 TO 9999: ";m16368,0m(16384)128ī1450m(16384)155ī700:INTROn(16384)141E LINE"l9,157:ABlA$"@SO IT CONTRIBUTES 4 TO CHI-SQUARE."Pl9,167:Al A$" T@HE RIGHT POINT IS 3 @SD@ FROM THE LINE"l9,179:AlA$" @SO IT ADDS WHAT TO CHI-SQUARE? "l(9,189:Al2A$l<A$(27)ī700:INTROmFA$"9"ĺ(7);1100!kt---------------EXAMPLE *k~:3Ck28,828,144272,144Uk38,144172,0fk72,4572,85wk71,6573,65k122,135122,95k121,115123,115kA$"SD"k8,59:9,78:A4k8,59:9,98:A4lA$"T@HE LEFT POINT IS 2 @SD@ FROM THR SEMI-LOG, PRESS @X@ AFTER LINEAR PLOT."7j9,165:AdjA$" T@O GO BACK OR ESCAPE, PRESS @ESC."rj$9,177:Aj.A$" T@O PROCEED, PRESS @RETURN."j89,189:AjB16368,0jLA$jVA$(27)Ĺ104,12:10j`A$"?"ī3570kjA$(13)ĺ(7);:0|dr5632d|103SCAPE, PRESS @ESC."!9,143:AI"A$" F@OR SINGLE FRAME, PRESS @S."W,9,155:A~6A$" T@O PROCEED, PRESS @RETURN."@9,167:AJB0ĺ(4)"BLOAD BDIPSHAPE":(4)"BLOAD BDIPOLE":B1TA$^A$(27)Ĺ104,12:10h5632r1061'A$"@CENTER, ORIENTED VERTICALLY."49,99:AeA$" T@HERE ARE 64 DIFFERENT PICTURES IN A"s9,111:AA$"@HALF-CYCLE, AND THEY ARE DISPLAYED AT"9,121:AA$"@THE RATE OF EIGHT PICTURES PER SECOND."9,131:AA$" T@O E." Z9,47:A? dA$"(T@HE MAGNETIC FIELD LINES ARE CIRCLES"L n9,57:A xA$"@PERPENDICULAR TO THE SCREEN.) (@S@EE @AJP" 9,67:A A$"49, 185 (1981).)" 9,77:A 0,7912,79 A$" T@HE INFINITESIMAL DIPOLE IS AT THE"9,89:A (233)28Č50688! :3M A$" R A D I A T I N G D I P O L E"` 9,9:A6981:A (A$" R H G@OOD 1983" 29,23:A <A$" T@HIS PROGRAM DISPLAYS THE ELECTRIC" F9,37:A PA$"@FIELD LINES OF A RADIATING ELECTRIC DIPOLE    (Y(I)YL):SS(I)Y(I)%| 2660:PLOT+| 9| RY010RBI| 2790:CALC[| 2900:THPLOTq| M(MTHRM.5)RM| B(BTHRB.5)RB|* 21:1|4 "Y = "YL" EXP(MX + B)"|> " = "YL" EXP("M" X ";|H B0ĺ"+";|R B")"40);|\ 16368,0|f A$D 2450:DRAW N${N YNYM*{X YM(YMYL)4{b YIYL={l X29N{v IYIRYL10k{ Y150(IRYLYL)142YM{ Y7ēX,YX2,Y{ { X23:YY2{ RYL10RYL:YIRYL{ N$(YI){ Y18Y145İ2450:DRAW A${ Y10ī3180{ I1N| XX(I):Y-LOGz 21:41)(z 7132:P.1 TO P.2:z 62450:CLEARMz 2310:X TICKS]z 2580:AXEStz A$"SEMI-LOG PLOT"z X180:Y6z 2480:DRAW A$z YLYM2YLYM2z RYL("1E"(((YL)(10))))z& YL(YLRYL)RYLz0 N$(YL)z: X23:Y152{B9999y@ X$""yJ /yT -------------THPLOTJy^ MMTHXM142(YM244)_yh B150BTH142YMnyr X42404zy| YMXBy Y0Y159ēX29,Yy y 24:1y "UNCERTAINTY IN M, "(DMRM.5)RM"; IN B, "(DBRB.5)RB"."40);y z ----------x X,YSX,YSx /x ---------------CALCWx RM("1E"(((XMYM)(10)2.7)))~x RB("1E"(((1YM)(10)2.7)))x DWXXWXWXWx D0ĺ(7);:1650x MTH(WXYWXWYW)Dx BTH(YWXXWXYWXW)Dx" DM(WD).5x, DB(XXWD).5y6 C,158w< 4829,158wF 1wP --------------PLOTDwZ YSYLYLYSTwd WW1(SS)fwn XWXWX(SS)xwx YWYWY(SS)w XXWXXWXX(SS)w XYWXYWXY(SS)w X244XXM29w Y150Y142YMw SS142YMw X1,YX1,Yw YSēX,0X,YS: (N$)1N$N$".0"$v A$(N$,4)6v I(A$)11Iv A((A$,I,1))Tv AX,Ydv A77XX2nv XX7tv zv v ----------------AXESv 4822,152v YL9999v 8922,81v W0:XW0:YW0:XXW0:XYW0v( 28,828,150272,150w2 88150uX,YX1,YuuXX2%u2u N$(YM)@u X23:Y10Su 2450:DRAW N$[u$ 22eu. Y149qu8 I110uB XM19A(I)ĂuL X28272A(I)243.9XMuV X,YX,Y1u` uj YY2ut u~ N$(XM)u X277:Y158u ---------------DRAW N$vSD("I"): ";t\X","Y","S*tf2640:PLOT0tpAtz1630:INPUTYt-------------TICKSkt62450:CLEARqtt35,23:TEXT WINDOWt24:"TO DELETE, D. TO PROCEED, PRESS RETURN."tX28tI110tYM19A(I)ĂuY1508A(I)141.9YM$7C77CCCCCC $$$$$$777777CCCCCC $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $7C $$$$$$$$$$$$777777777777777777777777777777777777CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC $$$$$$777777CCCCCC $$$$$$777777CCCCCC $$$$$$777777CCCCCC $$$$$$777777CCCCCC $$$$$$7777_?00L 0&&LF0@0LF0@0F0@0`F0@0L 0&&L'&%$#"!   $$$$$$$$$$$$$$$$$$$$$$$$(&FiGi'&FFP&FPGiG'i,ϥFiFGiG&i&'i,P&&F'GiР`@ `P0pH(hX8xD$dT4t L,l\<|B"bR2r J*jZ:zF&fV6vN.n^>~A!aQ1q I)iY9yE%eU5u M-m]=}C#cS3s K+k[;{G'gW7wO/o HxHZL6050.0&&x? 70&&PN 70&&(] C ؐb0HЎ0 d U  T@捽) (@?P??,̥i'&@0L_     %+*++1V^ѲQW\\ѥV]1UUUUPP1UVPWVѲ׳s+%%$%,2VVVVVVVVVV{]в׳~+*+*$%%+PVWЬ׳2\\{WV\V\\{++%++1VѲVWz\zV^1UUUUUP1UVPV\]^ѭץy%+%*$*%%%+,VW]Эѳ2WW\\WV\W\O+%+%++23вѭP{]\{]V]1UUUPPP1V2VVW{Ѳ+%%$$%+12VVVVVVVVVW\+%+%$*%&,VWЬѭ׳2\\\zzVzW\Эs+1PPPPP21V2VWWвѳ%*%$$$%,12VVVVVVVVV\{s*+%*%*%*+PVWѲ׳2WWWWVzWW]+*++%+,2]Э2z{]\V\1PPPPP21V2VVzЬѳs*+$%$$$%+P22VVVVVVVVVW]2Vzzz\WW\++%*+*+,2Wѳ2z{]]VW1PPPP221VPVz]^Э%***%%,P2P\VVVVVVV{]вѳ؀+%%%%$*%%1Uzввѳ2Vzzzz\WW{ѳy+*+*+%+1V|ѭ2z{{{VW$%+,2V2PVVVVVWVW\++%%%%+28Wѭ׳2Vz\\WWW\؀+%+*+%+1VW2\{]QW1PPP22222U\Vm%%**%,2P2PV\VV2WVV{ѳs+*+%%%++Uz{ѳ+*+12WЬ2\\]P{]1PP222222VV{]вѲѥO*%%$%%%,1VV2PVVVVV\V\{Ь~++%%%%%,1\]вѭ׳2V\\WWWW]c+%+%+%+P2ץ2\]]]{ѥQW1PP222222VV\{%%%%%\V{]Э*+*%%%++U\]Э׳2V\WWV{W{*+++*+OV]вѳ׳2\\P{]1PP22222PVW\~++%$$%+P2V2PVVVVV\V\вѳ++%*%%**,28\ѳ׳2V\WWWWW]ѥO+֥2W\{{2z1P222222VVW\Ь%*%%+PVVW22VVVVVzW\ѳy%%**%%%%+23WѲ׳2VWWVz{\y%+++12VвѲ2\\{{2z1P222222UVz{+%+%$$$$*,,PVz2PVVVVV%%%,23W2VWVzz{]++++OPWѭ׳2WW{{2z1P222222VV\{в׳s%*+$*11VVW\22VVVVVzW]*+*+1Pz{Ьвѳ2VWVzz{\s*+*+*+OU]PV\\׳22VVVVWV{]m+%**%%*%+,PzЬЭѲѳץ2VWVzz{{~++*++%O2WcвѲ׳2WW]]2z1P222222VV{]Ѳ%%$$*+1PVV{]Эѭ22VVVVWV\{+%**%2WW]]2z1P21V22VVV{ѳ%*%$$$$$%%,1UWV{ѭ׳22VVVV\V{ѳ++***%*+,P\{Эв2VWVz{\֥++++%O2VЭѲ׳2WW]]2z1P21V22PV\\s+%+1cЭ׳2VVzz{]s+++++PW2WW]]2z1P21V2PVVW]s%%*++UVVW]]Э׳~+%+%*22VVVVzW\ѥy+%*%+P2zѭѳ2VVzz{\в؀++*+++,P{Эѳ%+*%%%$$22VVVWV\ѥy+%%%%*++UW\вѲ׳2VVzz{]ѥO+*+++,2W2WW]]2z1P21V2PVV\Ѳm%%%$%$$%122VW\Ѳ׳s++$%%%$$22VVVVz\{+%**%%%%1P\]OPPWV{ЬѲѲ׳+*+%%$$22VVVWV{]ѳm+%+%%%%+,P\]Ѳ؀++%%%%2VVzz{{+++++,V]׳2WW]]2z{1P2222PVV{]ѳ%%*$$$*+,22V\{Ьѭրd11P2222VVV{Э~+%$$$$$%+P23V\ѲѲ׳%*+$%%$$$22VVV\W\+**+%$**+1P\]cвѳ+*+%%$%2VVz{\y+*++++U\2WW]2z1P2222PVz\Э׳+**%$$$                F DATA ARE NORMALLY DISTRIBUTED, THEN"39,59:AeA$"@ABOUT 1/3 OF THE POINTS LIE MORE THAN O"r9,69:A267,65269,65A$"@FROM , AND ONE POINT IN 2@O@ FALLS MORE"р8938,79:8939,791346,81:1347,819,79:AA$"@@ IS THE MEAN""8104,23106,23<B94110,27:94111,27TL1366,29:1367,29nV13188,29:13189,29{`9,27:AjA$"@AND O IS THE STANDARD DEVIATION (ALSO"t9,37:A~33,3335,33A$"@CALLED @SD@ HERE)."9,47:A&A$" I@"; Y0 = "(YL(BTH)RY0.5)RY040)0~ 3420K~ -----------------INFO[~ :3:A6981~A$" T@HE NORMAL OR @G@AUSSIAN DISTRIBUTION FOR"~9,7:A~A$"@RANDOM ERRORS IS OF THE GENERAL FORM"~$9,17:A.A$"@EXP(-(@Y-Y )^@/2O ), WHERE @Y!}p A$(27)YMYN::2060:LIST5}z A$(13)ī3500C} 16299,0K} A$Y} 16300,0k} A$"X"ī3420v} 23:1} "----------------------------(PRESS ESC)"} "X(1/2) = ";} MTH0ĺ"INFINITY";:3550} (69315(MTHRM).5)RM100000;&~ "j9,189:A"j70,19182,1914j16368,0:A$Vj16299,0:230,64:290:INPUTA$sj10:INTROFIC RADIATION (E.G. LIGHT).")i9,145:AYiA$" T@HE RADIATION IS POLARIZED WITH ITS"gi9,157:AiA$"@ELECTRIC FIELD VECTOR IN THE SAME PLANE"i9,167:AiA$"@AS THE ACCELERATION VECTOR."i9,177:AjA$" S@EE @AJP 52, 1150 (1984).LOSE TO THE CHARGE, THE LINES POINT"2hH9,103:A\hRA$"@AWAY FROM ITS CURRENT POSITION."jh\9,113:AhfA$" T@HE INTERVENING REGION OF TRANSVERSE"hp9,125:AhzA$"@FIELD MOVES OUT AT SPEED C; IT CONTAINS"h9,135:AiA$"@ELECTROMAGNET g9,51:AA$" C@THE"f9,9:ABfA$"@FIELD LINES POINT STRAIGHT OUT FROM IT."Of9,19:AfA$" I@F IT ACCELERATES, THEN AT A DISTANCE"f9,31:AfA$"@BEYOND CT (WHERE C IS SPEED OF LIGHT AND"f9,41:AgA$"@T IS TIME SINCE ACCELERATION) THE LINES"eA$(13)A$"K"`eA$"K"Ĺ143,255:A$" @V/C = @P@RESS @I@ OR @M.":490ie370oe}e9,191:Aee7135e4096e&10:INTROev-------------------INFOe:16302,0fA$" W@HEN THE CHARGE MOVES UNIFORMLY, d|N120#d(16384)128ī420)d2d370:dA$TdA$(27)Ĺ104,12:10kdA$"?"ī630:INFOdA$"0"Ĺ143,0:A$" @V/C = @U@SE @P@ADDLE(0).":490dA$"1"Ĺ143,1:A$" @V/C = @U@SE @P@ADDLE(1).":490BLOAD BMOVING".cBSAVE BMOVING,A$1000,L$900Hc"---------------INPUThc,A$"C@HOOSE: PADDLE (0)"vc69,151:Ac@A$"@PADDLE (1) (SMOOTHED)"cJ8,79:9,163:A4cTA$"@OR KEYBOARD (@K@)"c^8,29:9,175:A4ch16368,0cr95170,175A$" F@OR MORE INFORMATION, PRESS ?."4b9,101:A[bA$" F@OR SINGLE STEP, PRESS @S."ib9,113:AbA$" T@O GO BACK OR ESCAPE, PRESS @ESC."b9,125:AbA$" T@O PROCEED, PRESS @RETURN."b9,137:Ac(4096)169(6399)127ĺ(4)"GE MOVING ARBITRARILY IN"&ad9,47:AZanA$"@THE VERTICAL DIRECTION. (@N@INE PICTURES"gax9,57:A~aA$"@PER SECOND.)"a9,67:AaA$" (M@AGNETIC FIELD LINES ARE CIRCLES"a9,79:AaA$"@PERPENDICULAR TO THE SCREEN.)"a9,89:A&bW `(104)96Č506885` ------------------INTRO>`:3a`A$"M O V I N G C H A R G E"|`(8,43:9,9:A6981:A4`2A$"R H G@OOD 1983"`<8,85:9,23:A4`FA$" T@HIS PROGRAM DISPLAYS ELECTRIC FIELD"`P9,37:AaZA$"@LINES OF A CHAR     628nPA$"@WHERE @N@ IS NUMBER OF ATOMS, K IS @B@OLTZ-"FnZ9,176:AtndA$"@MANN'S CONSTANT, AND @V@ IS VOLUME."nn9,186:Anx16368,0:A$n370AND @V@ IS VOLUME."nn9,186:AnxA$n230,64:16299,0:370A0 A$700:INTRO55,15461,14862,148GA$"@D + ^D, WHERE D + 2 IS THE NUMBER OF"Z14,16319,163h9,163:A{34,15542,155A$"@POINTS; EITHER TOO LARGE OR TOO SMALL A"9,173:AA$"@VALUE OF CHI-SQUARE IS SUSPECT."9,183:A16368,3,11735,117Z62,11370,113PdA$"@PECTED ON THE SCALER (NOT COUNT RATE)."^n9,131:AxA$" I@F THE LINE FITS THE POINTS, THEN CHI-"9,143:AςA$"@SQUARE ( @^@) SHOULD BE APPROXIMATELY"݂9,153:A55,14857,14860,15462,154THAN 2O FROM THE LINE."$9,89:A5 47,8549,85eA$" R@ANDOM EVENTS COUNTED WITH A SCALER"s9,101:A(A$"@ARE GOVERNED BY THE @P@OISSON DISTRIBUTION,"29,111:A<A$"@AND O = ^@N@, WHERE @N@ IS THE NUMBER EX-"F9,121:A P3_?$0` 0` 0` 0` 0`'&%$#"!  @ `P0pH(hX8xD$dT4t L,l\<|B"bR2r J*jZ:zF&fV6vN.n^>~A!aQ1q I)iY9yE%eU5u M-m]=}C#cS3s K+k[;{G'gW7wO/o  0` 0` 0` 0` 0` 0` 0` 0` 0` 0` 0` 0` 0` 0` 0` @>@s>M@>Ms>T@>Ts>_@>_s>i@>is>s@>ss>~@>~s>@>s>@>s>@>sM((((((((((((((((((((((((((((((((PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP                        M>s>@>s>@>s>@>~s>~@>ss>s@>is>i@>_s>_@>Ts>T@>Ms>M@>@s!/:DLT\cjqx~Ԩ +@YxNmȾmN $*06CGKNRUXZ]_bdfhikmnpqrtuvwx1ƌ&'ɍSL0ɛ`ŋL0i'Յ&&'i')0 ''>& e4F  F  报FiIɥid'Յ&&i'i')0 LL0'@&@&& &&& & kg}}PI0p'@&@&& &&& &  LP UT 榏0, &*&!iejũ*T~LP plg}}PI0p'@&@&& &&& & plg}}PI0p _0LBiUi T R R RLZVRNJFB>`n@ V< Vd V V V V= Ve V V V V@ VnX`  eieP I0pƍ                CITY EXCEEDS"m9,177:ALmA$"@WAVE VELOCITY OVER MOST OF THE PACKET."Zm(9,187:Alm216368,0:A$tm<20, THEN @DX = 1."l9,133:AQlA$" N@OTE THAT FOR A GIVEN @T@, WAVE LENGTH"_l9,145:AlA$"@DECREASES AS @X@ INCREASES; THE HIGHER-"l9,155:AlA$"@MOMENTUM COMPONENTS ARRIVE FIRST."l9,165:A m A$" I@F @P > DP@ THEN GROUP VELOINCIPLE BECOMES"kt9,93:AQk~A$"DP * DX = @H/4@]@ = 1/2 FOR THE @G@AUSSIAN"_k9,103:AkA$"@PACKET AT @T@ = 0; @DP@ AND @DX@ ARE THE"k9,113:AkA$"@MOMENTUM AND POSITION UNCERTAINTIES."k9,123:AlA$"F@OR EXAMPLE, IF @DP@ = .59,39:A+jA$"@MOMENTUM AND @T@ TIME."8j$9,49:Akj.A$" T@HE AVERAGE DE @B@ROGLIE WAVELENGTH IS"xj89,61:AjBA$"@H/@P@; FOR EXAMPLE, WHEN @P@ = 3 IT IS 2.1"jL9,71:AjVA$"@UNITS IN @X."j`9,81:AkjA$" T@HE @U@NCERTAINTY @P@RNFOi:16302,0:3HiA$" I@N THIS MODEL, @P@LANCK'S CONSTANT IS"[i9,7:A6981:AiA$"@H = 2@]@, AND MASS M = 1."i9,17:AiA$" T@HE POSITION OF THE CENTER OF THE"i9,29:AiA$"@PACKET IS @X = PT@ (SINCE M = 1), @P@ BEING" j>---------------CALC"hH24:261hRSPP20.01?h\DDPDP2vhfDP0ē0,79256,79:0,154256,154:21:"ANY";:350hpDP2TM4:S15:920hzS110hP2TM7:930hTM12.7P:930hP2TM11.3Ph4096:$1000h350i-------------I(g5)"0"19)"5"24)"X AXIS"33)"10";9gX1025120JgX,156:X,81Pgeg130,157:130,82g28230,83:28230,158gA0Ĕ82122,55:5129,55g A63Ĕ73120,55:13129,55g31139,55g 31121,130g*42129,130g431139,130h)B$(8)B$"I"B$"X"B$"?"A$B$:410HfDB$"0"B$"9"ĺ(7);:560UfNA$A$B$`fX(8);mfbDP(A$)zflDP", ";fv17)"T = 0 ";:T0f---------------GRIDf:2f0,155256,155f256,800,80f3f30,1030,158g21:1)ī490eA$"?"ī9506eA$"0"A$"6"ĺ(7);:370BeP(A$)SeP", DP = ";[eA$eA$(27)A$(8)A$"I"A$"X"A$"?"ī410eA$(13)ī620eA$"."(A$"0"A$"2")ĺ(7);:500eA$"0"A$"2"ī610e&".";e0B$)f:B$(27:S373:SP20P(d^--------------INPUT0dhA0;dr24:1Rd|"P = ";:16368,0ZdA$ydA$(27)D30Ĺ104,12:10dA$(27)ī20dA$"I"A63:26:A$;:370dA$"K"Ė26:A$;:7132:370dA$"X"Ĺ16299,0:A$:16300,0:370eA$(13ESC."c9,134:A:cA$" T@O PROCEED, PRESS @RETURN."Hc"9,146:Alc,A$" L@IMITS: @P = 6, DP = 2."zc69,158:Ac@(4096)162ĺ(4)"BLOAD BFREE":A$1000,L$B00cJA0:D0:D10:D20:D30:D40:DP.5:DT.05:P3:PT0:T0:TD0:TM0dTS15:S250 F@OR MORE INFORMATION, PRESS ?.".b9,88:AUbA$" F@OR SINGLE STEP, PRESS @S."cb9,100:AbA$" T@O KEEP A PICTURE, PRESS @K."b9,112:AbA$" T@O SEE THE KEPT PICTURE, PRESS @X."b9,122:AcA$" T@O GO BACK OR ESCAPE, PRESS @"@DENSITY AND THE REAL PART OF THE PROB-"6an9,44:AgaxA$"@ABILITY AMPLITUDE OF A @G@AUSSIAN WAVE"ta9,54:AaA$"@PACKET IN ONE DIMENSION. (7 FRAMES/SEC.)"a9,64:AaA$" F@OR THE IMAGINARY PART, PRESS @I@ FIRST."a9,76:A!bA$" u `(104)96Č50688*` 28665:$6FF9D`---------------INTROQ`:::3y`(A$" F R E E P A R T I C L E"`29,7:A6981:A`<A$"R H G@OOD 1983"`F8,77:9,21:A4`PA$" T@HIS PROGRAM DISPLAYS THE PROBABILITY"`Z9,34:A)adA$     N IN RAPID MOTION." b9,47:APbA$" T@HE CLOCK MOVES AT SPEED V WHICH IS"]b9,59:AbA$"@NOT NECESSARILY SMALL COMPARED TO C, THE"b9,69:AbA$"@SPEED OF LIGHT. @I@T PRODUCES DOTS AND"b9,79:AcA$"@CLICKS AT UNIFORM PROPER T:TM100"a(----------------INTRO5a2:16302,0:3ea<A$" R E L A T I V I S T I C M O T I O N"qaF9,9:AaPA$"R H G@OOD 1984"aZ8,84:9,23:A4adA$" T@HIS PROGRAM ILLUSTRATES TIME DILATION"an9,37:AbxA$"@AND @L@ORENTZ CONTRACTIOv`(104)96Č50688*` 36864:$9000`A$"A":A6981:BX0:BYBX:PX.0001:PYPX:TC0:G1:X153:Y94:Z8445975:G0G:X0X:Y0Y:Z0ZaG11.2:G21.7:G32.5:G44:T1.22:T2.67:T31.5:T44.5:DP.1:YE160:XM279:YM191:RO.005:FF.027:GH1:TBTC:DT.14 37;??<:86420/.-,+*))(('''&&&&%%%%$$$$$$$###########"""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ~xsmga\VPJD>81+%  $(,048< $(,048"&*.26:>#'+/37;?#'+/37;? $(,048< $(,048"&*.26:>#'+/37;?#'+/37;? $(,048< $(,048"&*.26:>#'+/37;?#'+/((((((((((((((((((((((((((((((((PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP %+18>DJPV\agmsx~  !!"#$$%&''()*++,-./01123456789:;<=>?@ABCDEFGHIJKLMNOQRSTUVWYZ[\]_`abdefgijklnoprstvwyz{}~}{zxwusrpomkjhgedba_^\[YXVUTRQPNMLJIHFEDCB@?>=<;9876543210/.-,+**)('&%%$#"!!  ~}||{zyxwvuutsrqponmlkjihgedcba`_^\[ZYXVUTSQPOMLKIHGEDCA@>=;:976431/.,+)(&$#!  !$%')+,.01245689:<=>?@ABCDEFHHIJKLMNOPQRSTTUVWXXYZ[\\]^_``abbcdeefgghiijkllmmnoopqqrssttuvvwxxyyzz{||}}~~pH $ . H6ɛK U TLpH p3 祠pH +pV L'`E`EGfEeGjfEeGjfEeGjfEeGjfEeGjfEeGjfEeGjfEeGjfE`0Q&&JF0@0ejq5qqP&@'0Q&&qP&@'0Q&&Hejr5rr&@'0Q&&r&@'0Q&&00襋r5rr&@'0Q&&r&@'0Q&&00LL00捠e8刐 #Iip pJfEE*܈셎It 8<8刅F eFeF0E* 0JfEJfE pJfEJfEJfEJEjeF ) JJ0IiiPq5qqP&@'0Q&&qP&@' Pqrp 憏p: 憅0pH pr  憈pH p  !p]  憉 8叅 ꩓  p f !Ji@E 멓 f꩘ ƝE pk p + e L     #n 7139:16301,0:P.1 TO P.21n9415,10>n858,10gn(18,20:1415,20:422,20:6936,20vn2Y11549n<0,Y0,Y41,Y41,YnFnPS$""ī1480nZ---------------NEW V(X)ndW$"4"Č5120:1470nnX1279nxUSER'S V(X)o"A":X1:KE3394:DU0:E0:Y0:LL0:M5:MD0rmS1157:S2100:U0:U120:V0:VO0:C1144:XM279:H1200:YC79:YM158mW$((38399)):95FFmV(XM)mW$". HERE IS THE RIGHT HALF OF THE WELL.":m----------------GRIDm3mS$"X"đ:1310nAN EVEN FUNCTION (INITIAL @U@' = 0) THEN"7lV9,136:Ael`A$"@THE WELLS ATTRACT EACH OTHER, SINCE"slj9,146:AltA$"E@ INCREASES WITH SEPARATION @2S."l~9,156:Al149,158:1410,158ll-----------------INITl34816:$8800+mA$L):"k9,84:A0kA$"1411 V(X) = 80:S = 60"=k9,95:AjkA$"1412 IF ABS(X-S) < 40 THEN V(X) = 0"xk9,105:Ak$A$"@WHICH IS THE RIGHT HALF OF A PAIR OF"k.9,116:Ak8A$"@WELLS SHARING ONE PARTICLE. @I@F @U@ IS"kB9,126:A)lLA$"@A0jA$" X@ IS AN INTEGER BETWEEN 0 AND 279."=j9,42:AnjA$"V(X)@ IS 0 AT THE BOTTOM AND 158 AT THE"{j9,52:AjA$"@TOP OF THE PICTURE; BUT IT MAY EXCEED"j9,62:AjA$"@THESE VALUES."j9,72:AkA$" E@XAMPLE (MOLECULAR MODEī770i4A$"4"ī11801i>A$"5"ī2920:PAGE 5NiH-----------------PAGE 4WiR:3yi\A$"4: YOU CONSTRUCT A WELL."if8,35:9,6:A6981:A4ipA$"P@ROGRAM YOUR @V(X)@ ON LINES 1410-1420."iz9,20:AiA$"T@HEN TYPE @'RUN 1180'."j9,30:4 - 3394/X;"h9,165:A=hA$"4: Y@OU CONSTRUCT A WELL;"Kh9,178:AmhA$"5: D@ISCUSSION OF UNITS."{h9,191:Ah16368,0::A$h A$(27)Ĺ16300,0:230,32:360hA$"?"ī2510:PAGE 3h A$(13)A$"1":38399,49i*A$"1"A$"5"4:AgvA$" C@HOOSE:"&g9,116:AYgA$"1: S@QUARE WELL, @V(X)@ = 0 FOR @X < 157,"gg9,129:AgA$"@100 FOR @X >= 157;"g8,150:9,139:A4gA$"2: H@ARMONIC OSCILLATOR, @V(X) = X^/200;"g9,152:A hA$"3: C@OULOMB WELL, @V(X) = 14PPROXIMATION."f9,56:AEf&A$" T@O SUPERPOSE PLOTS, PRESS @S."Rf09,68:Af:A$" T@O REVIEW PREVIOUS VALUES, PRESS @T."fD9,80:AfNA$" F@OR MORE INFORMATION, PRESS ?."fX9,92:AfbA$" T@O ESCAPE OR GO BACK, PRESS @ESC."gl9,10DEL"e9,16:ACeA$"@CANNOT ACHIEVE PERFECT ACCURACY, SO OUR"Pe9,26:AeA$"U@ ULTIMATELY DIVERGES UP OR DOWN. @W@E"e9,36:AeA$"@BRACKET THE EXACT NTH ENERGY LEVEL @E "e9,46:Ae14250,48:14251,48fA$"@BY SUCCESSIVE A(4)"BLOAD BSCHR"dh:21.dr16368,0:A$Hd|A$(27)Ĺ104,12:10bdA$"?"ī2510:PAGE 3d-----------------PAGE 2d:3dA$" F@OR A BOUND PARTICLE @U@ SHOULD APPROACH"d9,6:A6981:AeA$"@THE @X@-AXIS ASYMPTOTICALLY. @T@HE MO9,140:AA$" F@OR SINGLE STEP, PRESS @S."iH9,178:AiR16368,0:A$i\A$"T"ī1280ifA$"G"Ĺ16300,0:230,32:380 jp---------Y A"h9,104:ADhA$"@FACTOR OF @\@, REGARDLESS OF DIRECTION."Rh9,114:AhA$"(T@HUS THE DISTANCE BETWEEN THE DOTS"h9,124:AhA$"@IS PROPORTIONAL TO @[\.)"h9,134:AhA$" L@ORENTZ CONTRACTION: THE CLOCK SHRINKS"i9,146:AREASES, THEN @[@ MAY"#gX9,72:A;gb2481,74:2482,74Ugl25212,74:25213,74ygvA$"@DECREASE CORRESPONDINGLY."g9,82:AgA$" T@IME DILATION: THE TIME BETWEEN CLICKS"g9,94:Ag14,9699,96hA$"@OF THE MOVING CLOCK INCREASES B0fA$"@OR Y COMPONENT OF @[\ @IS INCREMENTED"=f9,30:AOfA$"@BY +.1."\f9,40:Amf21,4026,40f&A$" I@N AN INERTIAL FRAME OF REFERENCE,"f09,52:Af:A$"@V CANNOT EXCEED C. @T@HUS IF THE X"fD9,62:AgNA$"@COMPONENT @[@ INCA$eA$(27)Ĺ104,12:100eA$(13)ī1680AeA$"G"ī880SeA$"T"ī1280eeA$"?"ī380e ---------------INFO?eeA$" B@Y PRESSING @I, J, K, M, @ONE APPLIES"e9,10:AeA$"@A FIXED IMPULSE TO THE CLOCK: THE X"f9,20:A @T."d,9,143:AAd6A$" F@OR FURTHER INFORMATION, PRESS ?."Od@9,155:A}dJA$" T@O GO BACK OR ESCAPE, PRESS @ESC."dT9,167:Ad^A$" T@O PROCEED, PRESS @RETURN."dh9,179:Adr(4096)169(6641)54ĺ(4)"BLOAD BREL"e|16368,0:IME INTERVALS."c9,89:ADcA$" W@E EMPLOY V/C = @[@ (BETA)"Rc9,103:A|cA$" @AND 1/^1-@[^ = \@ (GAMMA)."c9,117:Ac106,10876,109cA$" F@OR ACCELERATED FRAME, PRESS @G."c9,131:Ad"A$" F@OR @T@WIN @P@ARADOX, PRESS 레 *0(  砈 須] +레d ed ꠈ 륡G ꠈ G W] ꠈ 륡G 륡G :] ꠈd +i  砈 +레r L`lki2*H A 𠈩H `y ꠈ fꠈ  ` ꠈ fꠈk `i +레  砈 +레rLlki  ꠈ 須, f 砈] +레 !  TIME INCREMENT(n2T0:TIME SINCE PLOTGn<T10:T20:T30:TOTAL TIME`nF--------------GRIDSpnP:16302,0nZ28,128:62454nd5:27236,170nn6:0236,179nx3nXC4,YCXC5,YCnXC,YC3XC,YC3XC1,YC3XC1,YC3:"+"o6,153121)(Z3Z1))]mR120((R230R310)N3)ĺ(7)8)"TWO BODIES COINCIDE.";:A$:1:868:1080xm-----------------ETC.mI230:J16336:JN16384m MMM2:M3M2MMM3mDV100P:MAXIMUM VELOCITY INCREMENTmK.5(100P):FORCE CONSTANTn(DT0::V2(V$(N)):W2(W$(N)).lX1(M2X2M3X3)DlY1(M2Y2M3Y3)ZlZ1(M2Z2M3Z3)lR12((X1X2)(X1X2)(Y1Y2)(Y1Y2)(Z1Z2)(Z1Z2))lR23((X2X3)(X2X3)(Y2Y3)(Y2Y3)(Z2Z3)(Z2Z3)) mR31((X3X1)(X3X1)(Y3Y1)(Y3Y1)(Z3Z25NkL1910:GET DIGITS.kVN2M30:1170:k`K4:23Pkj1910:GET DIGITSdktM3(M$(4))100k~X3(X$(4)):Y3(Y$(4)):Z3(Z$(4))kU3(U$(4)):V3(V$(4)):W3(W$(4))kM2(M$(N))100kX2(X$(N)):Y2(Y$(N)):Z2(Z$(N))lU2(U$(N))R WITH ARROWS.",j:"DEFAULT PARAMETERS:"Vj6)"M X Y Z VX VY VZ"j$"M2:"4)M$(N)9)X$(N)14)Y$(N)19)Z$(N)24)U$(N)29)V$(N)34)W$(N)j.N3ĺ"M3:"4)M$(4)9)X$(4)14)Y$(4)19)Z$(4)24)U$(4)29)V$(4)34)W$(4)j8AM100kBKN:50?iG$((.5100(10(2P(2P))))100)"E"((2P2))liG(G$):G1000000G$(G):P=100^(-P-1)i:"GRAVITATIONAL CONSTANT G = "G$"."i----------------M,V,R,iiK0ī1050i"PARAMETER LIMITS: -100 TO 100."j:"MOVE CURSO"2"N$"3"ī790hHN(N$)%hRN"."@h\-----------------P,G,FhfthpK0ĺ"THE FORCE IS PROPORTIONAL TO R^P."hz"DEFAULT P="P$"."18)"SET P=";hAM10:J5h1990:GET DIGITS hA$" "P$A$hP(P$)hP$"."iS$(8)S$(27)ī7,12:10gA$"?"ī2310:INFO3gA$(13)ī710Og----------------SET N,sg::"CHOOSE 2: TWO BODIES;"g11)"3: THREE BODIES: ";g 16368,0gN$g N$(27)ī370:INITg*N$"?"ī2310:INFOg4N$(13)N$(21)N$(N)h>N$.":/f"FOR FURTHER INFORMATION, PRESS ?.":Kf"TO ERASE, PRESS E.":uf"TO GO BACK OR ESCAPE, PRESS ESC.":f"TO DEFAULT OR PROCEED, PRESS RETURN.";f(4096)160(5476)234ĺ:(4)"BLOAD BTHREE"f16368,0fA$gA$(27)Ĺ104$(4)" 0":W$(4)" 0".e0---------------INTRO9e:::3feD"T H R E E B O D I E S I N 3 - D"eN:12)"RH GOOD 1983"eX:eb"THIS PROGRAM PLOTS ORBITS OF TWO OR"el"THREE BODIES MOVING UNDER THEIR"fv"MUTUAL GRAVITATIONAL ATTRACTIONRdM$(2)" 40"9dX$(2)" 70":Y$(2)"-70":Z$(2)" 10"^dU$(2)" 4":V$(2)" 4":W$(2)" 2"ndM$(3)" 10"dX$(3)" 83":Y$(3)" 0":Z$(3)" 0"dU$(3)" 0":V$(3)" 10":W$(3)" 0"dM$(4)" 0"dX$(4)" 73":Y$(4)" 0":Z$(4)" 0"e&U$(4)" 0":V32759:$7FF7c290"cA$"A"5cYS.9:Y-SCALENcXC139:YC91:CENTERcT10:X10:X20:X30:Y10:Y20:Y30:Z10:Z20:Z30cDT0:DV0:K0:M20:M30:N0:P0:R10:R20:R30:T0:U20:U30:V20:V30:W20:W30:MM0cN2:BODIESdP$"-2":POWEYCY3YSbI,32(b0XCX3,YCZ3YS2bI,64:b30Tb"-----------------ERR^b,7126sb6(218)190ī200b@(218)210ī220bJ(218)240ī250bT(218)4ī270b^(218)150ī160bh(218)170ī180brb|-----------------INIT c191:T3T31:T310T30an31axT148185,191_aT10ĔT248178,191:T20ĔT348171,191fa5}a27XCX1,YCY1YSaI,32a27XCX1,YCZ1YSa6a0XCX2,YCZ2YSaI,64a0XCX2,YCY2YSaN$"2"ī30a7b0XCX3,`(104)96Č50688'` 380:INITC`-------------CALCULATEj`ST$"S"(JN)128ī1810:KEYPRESSt`(4096`2T0ī30`<----------------PLOT`F4`PT148185,191`ZT1T11adT110T10:T248178,191:T2T21:T210T20:T348171,        !!! ! ! ! ! !!!!!!!!!""" " TIME 0" v 8,194:9,189:A4*v7135Bv A$"E@VENT HORIZON"Zv*6,0:S$"S"Ĺ6,211cv47,0mv>4096uvH10-0:S$uS$(27)ī40u04u8,90:9,182:A4Pu73261,173:73262,173lu77262,191:77263,191|uA$"C@LOCK"u8,167:9,97:A4u3uA$"\ = 1"u8,100:9,188:A4uA$"O@BSERVER TIME 0"u8,171:9,179:A4 vA$"C@LOCKt5434,76:5407:5434,32.t&A$" [ = .00"s128X,Y6128X,Y5Dsms130,90132,87134,90:131,89133,89s128,99136,99s127,100137,100sA$"O@BSERVER"s8,107:9,115:A4sA$"C@LOCK"s8,167:9,97:A4sXX0:YY0sX0,Y0RE TIMES."r69,159:AJr@A$" N@ON-INERTIAL OBSERVER: AS BEFORE, BUT"XrJ9,171:ArTA$"@PRESS @G@ BEFORE @RETURN@ AND DON'T USE @M."r^9,181:Arh16368,0:A$rrA$"?"ī440r|A$"G"ī880r16300,0:230,32:380s---------------q9,119:ABqA$"@CLOCK; RUN @[ @ UP TO .86; PRESS @RETURN,"Pq9,129:Ajq2584,131:2585,131qA$"@AND PRESS @M@ REPEATEDLY, 34 TIMES IN 13"q"9,139:Aq$A$"@SECONDS, UNTIL THE CLOCK RETURNS; PRESS"q&9,149:A r,A$"S@ AND COMPAINERTIAL REFERENCE" p9,73:ARpA$"@FRAME, SO TIME DILATION IS INSUFFICIENT"_p9,83:ApA$"@TO EXPLAIN HIS OBSERVATIONS."p9,93:ApA$" W@E CAN ILLUSTRATE AS FOLLOWS:"p9,107:AqA$" I@NERTIAL OBSERVER: PRESS @S@ TO HOLD THE"RIAL TWIN."oF9,29:AKoPA$" T@HE @T@WIN @P@ARADOX: IF ALL MOTION IS"XoZ9,41:Ajod42,43126,43onA$"@RELATIVE, WHY DO THE TWINS DIFFER?"ox9,51:AoA$" T@HE RESOLUTION: THE TRAVELING TWIN"o9,63:ApA$"@DOES NOT REMAIN IN AN  멘 驓  +렀  fꠀ Ɲ +렀 Ɲ    +L砀T +렀 ꠀ[ 頀# 砀# +렀 ꠀ[ 頀8 砀8 +렀 ꠀ[ 頀M 砀M +0* ꠀw  !렀# ꠀp 驓  +렀? ꠀw  !렀8 ꠀp 驓 1 +렀T ꠀw  !렀M ꠀp 驓 F +00L`  !렀* ꠀ  驓 砀 砀 +렀? ꠀ8   !렀? ꠀ1  驓 砀 砀 +렀T ꠀM   !렀T ꠀF  驓 砀 砀 +렀 ꠀ[ 頀* 砀* +렀 ꠀ[ 頀? 砀? +렀 ꠀ[ 頀T F  頀 砀 +LwL  頀w f  +렀# ꠀ*  頀 砀 +렀8 ꠀ?  頀 砀 +렀M ꠀT  頀 砀 +렀   f +렀  頀p f  +렀* ꠀ# !렀T ꠀF 碱   +렀[  + ꠀb 頀[ +렀  0 砀[ 砀[ +넝 +렀[  砀i  +렀   f +렀# ꠀ  頀 砀 +렀8 ꠀ1  頀 砀 +렀M ꠀ# ꠀ 멘  !렀8 ꠀ1 멘 驓 !렀M ꠀF 碣  +L#* ꠀ# 멘  !렀? ꠀ8 멘 驓 !렀T ꠀM 碪   f  +렀* ꠀ 멘  !렀? ꠀ1 멘 驓  THE TEMPERATURE AND""oJ9,18:AHoTA$"@IS INDEPENDENT OF THE MASS."Uo^9,28:AohA$" I@N 3 DIMENSIONS, THE SPEED DISTRIBUTION"or9,46:Ao|A$"@IS OF THE FORM"o9,56:AoA$"@V@^@EXP(-V@^@), WHICH IS"o9,66:A pA$"@ZERO AT SP THE"n9,179:AEnA$"@IDEAL GAS LAW, ITS ATOMS DON'T COLLIDE."Sn9,189:Aen16368,0:A$~nA$"X"A$"?"ī10n-------------INFO 3Dn"n,A$"T@HE AVERAGE KINETIC ENERGY OF THE ATOMS"n68,11:9,8:A4o@A$"@IS PROPORTIONAL TO8,188:9,141:A4,mx1:170,131270,131:39m171,130EmE099ZmD(25(E36))lm171E,130DrmmA$" F@OR DISTRIBUTIONS IN"m9,142:AmA$"@3-DIMENSIONAL GAS, PRESS @X."m9,152:AnA$" T@O THE EXTENT THAT A GAS OBEYS,75:3lV0100/l D(V(VV1600)1.2)Hl170V,74170V,74DNl|l(A$" T@HE CORRESPONDING DISTRIBUTION OF"l29,98:Al<A$"@KINETIC ENERGY @K@ IS OF"lF9,108:AlPA$"@THE FORM EXP(-@K)."lZ9,118:AldA$"@ENERGY @K"mnIONS, THE SPEED DISTRIBUTION"*k9,46:ACkA$"@IS OF THE FORM"Pk9,56:A\kA$"@V"ik9,66:AkA$"@EXP(-V@^@), WHICH IS"k8,17:9,66:A4kA$"@ZERO AT SPEED V=0."k9,76:AkA$"@SPEED"k8,190:9,84:A4l1:170,75270I" j$10$j.-------------INFO 2D4j8:16302,0hjBA$" A@FTER A MINUTE OF COLLISIONS, THE SPEED"tjL9,8:AjVA$"@DISTRIBUTIONS NO LONGER DEPEND ON WHETHER"j`9,18:AjjA$"@1 OR 2 WAS CHOSEN INITIALLY."jt9,28:Ak~A$" I@N 2 DIMENS E@SCAPE: @ESC."&i9,189:A6iA$"@SPEED"Mi8,243:9,110:A4di8,243:9,149:A4si0235,107i234,145235,145:233,146236,146:233,147236,147:234,148235,148iCLICK(16336)(16336)i4256:RUNj5120,166:CANCEL "h\:16302,04hf2:0,00,176226,176226,00,0]hp1:229,139279,139:229,100279,100nhzX2292794hX,101:X,140hh3hA$"COLLISIONS.":8,90h(5120)96A$"NO COLLISIONS.":8,80h9,186:A4iA$"S@TEP: @S. V10gPXPX7:PYPXDP g4gPX,V2:PY1,V2Ig----LARGE ATOMS[gI$"1"V027mgI$"2"V054{gV1256V0g PX36380100:PYPXDPgY04g X04g*PXX,V0X:PYX,V1Yg4g>PXPX5:PYPXDPgHhR----------------PLOT"2"I$"3"V027:V1251:V238:V3225:V419:V5218:V6242CfbDP256OflI013afvPX,V0:PY,V0wfPX1,V1:PY1,V2fPX2,V2:PY2,V1fPX3,V3:PY3,V4fPX4,V4:PY4,V3fPX5,V5:PY5,V63(1)fPX6,V6:PY6,V5gV1V11:V12565120,96&eI$"T"Ĕ84235,122:6,212>eI$"1"I$"3"ī400Te0:95190,190:3ge(I$)190,190e&---------------INITe04096:CLEARe:----SMALL ATOMSeDPX36380:PYPX256eNI$"1"V054:V1249:V273:V3192:V438:V5184:V62348fXI$ĺ(4)"BLOAD BGAS".d|----------------INPUT LdCLICK(16336)(16336)Zd16368,0jd95190,190vdI115d(16384)128ī460dd410dI$dI$(13)I$"2"dI$(27)Ĺ104,12:10dI$"?"ī1070eI$"I"Ĕ73200,110:EED, PRESS @RETURN.""c9,146:AQc"A$" C@HOOSE INITIAL SPEED DISTRIBUTION:"_c,9,158:Ac6A$" 1. S@MALL ATOMS FAST."c@9,170:AcJA$" 2. L@ARGE ATOMS FAST."cT9,180:Ac^A$" 3. B@OTH SLOW."ch9,190:Adr(4096)162,86:A2bA$" F@OR MORE INFORMATION, PRESS @?."?b9,98:AhbA$" F@OR NO COLLISIONS, PRESS @I."vb9,110:AbA$" T@O TRAIL A LARGE ATOM, PRESS @T."b9,122:AbA$" T@O ESCAPE OR GO BACK, PRESS @ESC."b9,134:AcA$" T@O PROCAME AVERAGE KINETIC"!ad9,46:AVanA$"@ENERGY MV@^/2. I@N THIS MODEL, THE LARGER"cax9,56:AaA$"@ATOMS HAVE FOUR TIMES THE MASS, SO THEIR"a9,66:AaA$"@AVERAGE SPEED BECOMES HALF THAT OF THE"a9,76:AaA$"@SMALLER ONES."b9,`(104)96Č506884` -----------------INTROK`::3:6,0:7,255Z`A$"G A S"v`(A6981:8,105:9,8:A4`2A$"R H G@OOD 1985"`<8,77:9,22:A4`FA$" A@T EQUILIBRIUM, GAS ATOMS OF DIFFERENT"`P9,36:AaZA$"@KINDS POSSESS THE S?MM<<,'%'%'%g%g-< ,666m3'''''%'%'%'%%5D.,666?o ><<<<,<'%'%g%%5%5%66?o ><<<<,<'%g%g%5%5%566oM<,'%'%'%'%g%g%5666o<,'%''%'%g%g5->66o2'''''%'%'%g5%5%vo3''7<<$'%5 ,.,.6?oMJJJJӤ 'JJJ`&EFI)%0Q&&e)j*0JI0`'0`0 I0ꩁ(0.',"&,Ci8i#H&ii&hif&i'`'i,&i,&iPII&if&<<<<,'%'%g%g%%5 ,0  ,ԐԠ `, `'І&FI`G&&Fȱ&F &,3Ɏ0 `L  # 4   扥i`   )%0&& BJJJ`A G: G &FIJK IJK $0b3 ꠐ fꠐ  !렐, 멓 砐, + #  !렐 砐 + # /LE%0Q&&`E''%0Q&& 0'Ѕ&&&ȑ& )𠐩 ꠐ, ebM0 ꠐ  ꠐI f 렐 0/  $ @ ` IIIJL3 ꠐk 1r "y  K JJL p& E)$p ,  ,3 ꠐ 碁  pI`GF&F E&,L$p"РSP'&E` {0. 4.  扥iƈ` ꠐ  !렐% ꠐ%   !Ji@H 멓 f꩘ ƝhJ점3 +렐 fꠐ +렐3 ꠐ% fꠐ +$0} 杠 預: 砐$ 0: +렐 杠  !렐A $0 0% 0A +L] GV G &Fefg efg  $P[$0.3 杠3 砐O Ɲ 預% 砐% +렐A 杠A 砐] Ɲ 祝8 +3OL UT Emɍɛ`I  % E ꠐE 砐%E ꠐE 砐E +L[ IP&I` ''Q&&$P6g Wm :g Wm :g Wm :`"""""""""ATION, SEE"9,179:ANA$"@THE PROGRAM BY @E. L@ANE, @C@ONDUIT 1985.)"\9,189:An16368,0:A$A$"X"ī10X(0)16300,0:A$A$"X"ī1016299,0:2210o A$"@ENERGY @K"+8,188:9,141:A48 170,130D*K199^4D(12(K)(K21))p>171K,130DvHRA$" F@OR DISTRIBUTIONS IN"\9,142:AfA$"@2-DIMENSIONAL GAS, PRESS @X."p9,152:A zA$" (F@OR MORE ON ATOMS IN ANIM,0:A$s A$"X"ī10+s16299,0:2020A"r9,142:A6rA$"@2-DIMENSIONAL GAS, PRESS @X."Dr9,152:AurA$" (F@OR MORE ON ATOMS IN ANIMATION, SEE"r9,179:ArA$"@THE PROGRAM BY @E. L@ANE, @C@ONDUIT 1985.)"r9,189:Ar16368,0:A$rA$"X"ī10rX(0)s16300q9,108:A.q&A$"@THE FORM ^@K@ EXP(-@K)."