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|00000000| 00 07 66 61 6c 6c 69 6e | 67 00 00 00 00 00 00 00 |..fallin|g.......|
|00000010| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000040| 00 54 45 58 54 4d 50 41 | 44 00 00 00 00 00 00 00 |.TEXTMPA|D.......|
|00000050| 00 00 00 00 00 03 8c 00 | 00 01 56 a8 c3 97 5c a8 |........|..V...\.|
|00000060| c3 97 5c 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |..\.....|........|
|00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 12 e4 00 00 |........|........|
|00000080| 2d 2d 54 68 69 73 20 65 | 78 61 6d 70 6c 65 20 73 |--This e|xample s|
|00000090| 69 6d 75 6c 61 74 65 73 | 20 61 20 66 61 6c 6c 69 |imulates| a falli|
|000000a0| 6e 67 20 6f 62 6a 65 63 | 74 20 77 69 74 68 20 61 |ng objec|t with a|
|000000b0| 69 72 20 66 72 69 63 74 | 69 6f 6e 20 70 72 6f 70 |ir frict|ion prop|
|000000c0| 6f 72 74 69 6f 6e 61 6c | 20 74 6f 20 74 68 65 20 |ortional| to the |
|000000d0| 73 71 75 61 72 65 20 6f | 66 20 69 74 73 20 76 65 |square o|f its ve|
|000000e0| 6c 6f 63 69 74 79 2e 20 | 54 68 65 20 74 65 63 68 |locity. |The tech|
|000000f0| 6e 69 71 75 65 20 75 73 | 65 64 20 69 73 20 69 6e |nique us|ed is in|
|00000100| 65 66 66 69 63 69 65 6e | 74 20 63 6f 6d 70 61 72 |efficien|t compar|
|00000110| 65 64 20 77 69 74 68 20 | 66 61 6e 63 69 65 72 20 |ed with |fancier |
|00000120| 6d 65 74 68 6f 64 73 20 | 66 6f 72 20 6e 75 6d 65 |methods |for nume|
|00000130| 72 69 63 61 6c 20 73 6f | 6c 75 74 69 6f 6e 73 20 |rical so|lutions |
|00000140| 6f 66 20 64 69 66 66 65 | 72 65 6e 74 69 61 6c 20 |of diffe|rential |
|00000150| 65 71 75 61 74 69 6f 6e | 73 2c 20 62 75 74 20 69 |equation|s, but i|
|00000160| 74 20 69 73 20 76 65 72 | 79 20 65 61 73 79 20 74 |t is ver|y easy t|
|00000170| 6f 20 70 72 6f 67 72 61 | 6d 2e 20 53 65 65 20 65 |o progra|m. See e|
|00000180| 78 61 6d 70 6c 65 20 22 | 70 72 6f 6a 65 63 74 69 |xample "|projecti|
|00000190| 6c 65 22 20 66 6f 72 20 | 61 20 73 69 6d 69 6c 61 |le" for |a simila|
|000001a0| 72 20 70 72 6f 62 6c 65 | 6d 20 69 6e 20 74 77 6f |r proble|m in two|
|000001b0| 20 64 69 6d 65 6e 73 69 | 6f 6e 73 2e 0d 0d 69 6e | dimensi|ons...in|
|000001c0| 69 74 20 3d 20 76 3a 3d | 30 2c 74 3a 3d 30 20 20 |it = v:=|0,t:=0  |
|000001d0| 2d 2d 20 69 6e 69 74 69 | 61 6c 20 63 6f 6e 64 69 |-- initi|al condi|
|000001e0| 74 69 6f 6e 73 0d 0d 73 | 74 65 70 74 6f 28 73 74 |tions..s|tepto(st|
|000001f0| 6f 70 29 20 3d 20 69 6e | 69 74 20 77 68 65 6e 20 |op) = in|it when |
|00000200| 73 74 6f 70 3d 30 2c 0d | 20 20 20 20 20 20 20 20 |stop=0,.|        |
|00000210| 20 20 20 20 20 20 20 28 | 76 3a 3d 76 2b 61 2a 64 |       (|v:=v+a*d|
|00000220| 74 2c 0d 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |t,.     |        |
|00000230| 20 20 20 74 3a 3d 74 2b | 64 74 29 20 77 68 69 6c |   t:=t+|dt) whil|
|00000240| 65 20 74 3c 73 74 6f 70 | 0d 0d 66 3d 6d 2a 67 2d |e t<stop|..f=m*g-|
|00000250| 6b 2a 76 5e 32 20 20 20 | 2d 2d 20 67 72 61 76 69 |k*v^2   |-- gravi|
|00000260| 74 79 20 2d 20 61 69 72 | 20 66 72 69 63 74 69 6f |ty - air| frictio|
|00000270| 6e 0d 61 3d 66 2f 6d 0d | 20 20 20 20 20 20 20 20 |n.a=f/m.|        |
|00000280| 20 20 20 20 0d 67 3d 39 | 2e 38 20 20 20 20 20 20 |    .g=9|.8      |
|00000290| 20 20 2d 2d 20 61 63 63 | 65 6c 6c 65 72 61 74 69 |  -- acc|ellerati|
|000002a0| 6f 6e 20 64 75 65 20 74 | 6f 20 67 72 61 76 69 74 |on due t|o gravit|
|000002b0| 79 0d 6b 3d 32 20 20 20 | 20 20 20 20 20 20 20 2d |y.k=2   |       -|
|000002c0| 2d 20 66 72 69 63 74 69 | 6f 6e 20 63 6f 65 66 66 |- fricti|on coeff|
|000002d0| 69 63 69 65 6e 74 0d 6d | 3d 33 30 30 20 20 20 20 |icient.m|=300    |
|000002e0| 20 20 20 20 2d 2d 20 6d | 61 73 73 20 6f 66 20 6f |    -- m|ass of o|
|000002f0| 62 6a 65 63 74 0d 64 74 | 3d 2e 30 35 20 20 20 20 |bject.dt|=.05    |
|00000300| 20 20 20 2d 2d 20 74 69 | 6d 65 20 73 74 65 70 20 |   -- ti|me step |
|00000310| 66 6f 72 20 73 69 6d 75 | 6c 61 74 69 6f 6e 0d 0d |for simu|lation..|
|00000320| 76 73 69 6d 28 74 31 29 | 20 3d 20 73 74 65 70 74 |vsim(t1)| = stept|
|00000330| 6f 28 74 31 29 2c 76 20 | 20 2d 2d 72 75 6e 20 74 |o(t1),v | --run t|
|00000340| 6f 20 74 31 2c 20 72 65 | 74 75 72 6e 20 76 0d 0d |o t1, re|turn v..|
|00000350| 58 6d 69 6e 3d 30 3b 20 | 58 6d 61 78 3d 31 30 20 |Xmin=0; |Xmax=10 |
|00000360| 20 2d 2d 20 70 6c 6f 74 | 20 76 20 76 73 20 74 69 | -- plot| v vs ti|
|00000370| 6d 65 20 66 6f 72 20 31 | 30 20 73 65 63 0d 70 6c |me for 1|0 sec.pl|
|00000380| 6f 74 20 76 73 69 6d 28 | 58 29 0d 0d 2d 2d 20 63 |ot vsim(|X)..-- c|
|00000390| 6f 6d 70 61 72 65 20 74 | 6f 20 61 6e 61 6c 79 74 |ompare t|o analyt|
|000003a0| 69 63 61 6c 20 73 6f 6c | 75 74 69 6f 6e 0d 76 61 |ical sol|ution.va|
|000003b0| 6e 28 74 29 3d 73 71 72 | 74 28 6d 2a 67 2f 6b 29 |n(t)=sqr|t(m*g/k)|
|000003c0| 2a 74 61 6e 68 28 73 71 | 72 74 28 67 2a 6b 2f 6d |*tanh(sq|rt(g*k/m|
|000003d0| 29 2a 74 29 0d 70 6c 6f | 74 20 76 61 6e 28 58 29 |)*t).plo|t van(X)|
|000003e0| 0d 0d 74 61 6e 68 28 75 | 29 3d 28 65 78 70 28 75 |..tanh(u|)=(exp(u|
|000003f0| 29 2d 65 78 70 28 2d 75 | 29 29 2f 28 65 78 70 28 |)-exp(-u|))/(exp(|
|00000400| 75 29 2b 65 78 70 28 2d | 75 29 29 0d 00 00 00 00 |u)+exp(-|u)).....|
|00000410| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000420| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000430| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000440| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000450| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000460| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000470| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000480| 00 00 01 00 00 00 01 24 | 00 00 00 24 00 00 00 32 |.......$|...$...2|
|00000490| 64 74 c0 5f 58 c8 02 22 | 54 2f 29 31 01 21 22 67 |dt._X.."|T/)1.!"g|
|000004a0| 83 01 b0 68 b1 67 01 67 | 2e 7f 7e 31 32 7a 9f 51 |...h.g.g|..~12z.Q|
|000004b0| 07 66 61 6c 6c 69 6e 67 | 02 00 00 00 50 61 72 74 |.falling|....Part|
|000004c0| 53 49 54 78 00 00 00 00 | 00 00 00 00 00 01 49 27 |SITx....|......I'|
|000004d0| 00 00 50 61 72 74 53 49 | 54 78 00 00 00 00 00 00 |..PartSI|Tx......|
|000004e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000004f0| 00 00 a9 7e bd ee 00 00 | 00 00 00 00 01 56 9d 67 |...~....|.....V.g|
|00000500| 8e 01 03 ca 99 02 65 78 | 74 6e 5a 5b 50 01 2f 02 |......ex|tnZ[P./.|
|00000510| 7a 5f 6d 80 01 03 b2 55 | 7a 01 ff 9e 59 5b 58 01 |z_m....U|z...Y[X.|
|00000520| 3d 68 b1 01 ff a2 76 11 | fe 8c 11 42 10 01 10 2d |=h....v.|...B...-|
|00000530| 11 fe 02 03 65 00 03 92 | 0c 00 e8 02 62 00 03 8a |....e...|....b...|
|00000540| 8b 06 12 00 d2 41 32 3b | 10 06 4e fb 10 00 75 06 |.....A2;|..N...u.|
|00000550| 00 34 00 82 00 b8 02 ac | 03 62 b9 fc 6c 6c b0 8d |.4......|.b..ll..|
|00000560| be 03 70 04 a5 22 28 48 | 8d 80 01 03 58 7f 03 42 |..p.."(H|....X..B|
|00000570| 50 21 cc 0b 64 12 1b 7c | 00 01 26 86 1a 28 18 48 |P!..d..||..&..(.H|
|00000580| 00 00 00 20 00 00 00 02 | 00 02 3f f9 8e fa 35 12 |... ....|..?...5.|
|00000590| 94 e9 c8 ae 01 2c 01 23 | 00 06 00 29 00 cc 01 24 |.....,.#|...)...$|
|000005a0| 01 33 00 28 00 00 01 00 | 00 00 01 24 00 00 00 24 |.3.(....|...$...$|
|000005b0| 00 00 00 32 00 33 34 a0 | 05 26 00 00 00 1c 00 32 |...2.34.|.&.....2|
|000005c0| 00 00 50 52 65 66 00 00 | 00 0a 00 80 ff ff 00 00 |..PRef..|........|
|000005d0| 00 00 00 34 1a 3c 00 00 | 00 00 00 00 00 00 00 00 |...4.<..|........|
|000005e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000005f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
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