TIInterActive FileHarmoniske svingninger De opdagelser I gr undervejs skriver I ned p et stykke papir ved siden af jer, s I har det til brug senere. Vi vil i det flgende kigge p funktioner af typen  hvor a, b, c og k er konstanter, hvor b > 0. Den simpleste sinussvingning vi har er, hvor a =1, b =1, c = 0 og k = 0.  Svingningstiden (eller perioden) er afstanden fra en blgetop til den nste, dvs. tiden hvor der er gennemfrt en hel svingning.  Prv udfra grafen at give dit bud p svingningstiden for . Hvis du nu tager en halv svingning og ser p den - hvilket tal minder det dig om? Giver det mening i forhold til din tidligere viden om sinus?  I det flgende skal I vha. af skyderne ndre grafernes udseende og komme med jeres bud p betydningen af de forskellige konstanter for grafen. Afprv hvad der sker, nr a ndrer sig. Hvad er as betydning for grafen?     Hvad betyder k-vrdien for grafen?     Hvilken betydning har b-vrdien?     Vi ser lige p b-vrdien n gang til. Hvad skal b vre for at svingningstiden er 1 henholdsvis 2?    Har du et bud p et generelt forhold mellem b og svingningstiden?  Vi ser p den sidste konstant c. Hvad er cs betydning for grafen?     Prv nu at ndre p bde b og c. b  c    Hvordan forskydes grafen i forhold til den rde graf for sin x?  Lav en opgave til din sidekammerat.Ved hjlp af skyderne skal du lave en graf som du giver til din sidekammerat. Han/hun skal s udfra grafen bestemme konstanterne a, b ,c og k. Husk at skrive ned hvad skyderne str p s du kan rette opgaven for din sidekammerat bagefter. For at gre det nemmere at aflse - kopier grafen (Ctrl c) og indst i word (Crtl v) - du kan nu trkke i nederste hjre hjrne, s grafen bliver lidt strre og dermed nemmere at aflse. a  b  c  k     Hvorfor snakker vi kun om grafer for sinussvingninger, burde vi ikke ogs snakke om grafer for cosinussvingninger? 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30000 50004 70006 2360008 cb0000 710000 0 0 0 1 0 1ffff 4743000a 6870796c 4854414d 146 8f 71 0 ffff 10000 0 10000 1ffff 4743000a 6870796c 574f524d 146 8f 71 0 ffff 10000 0 20000 1ffff 47430008 6870796c 145534d 8f0000 710000 0 ffff0000 0 1 0 800b0001 145 8f 71 0 ffff 10000 0 60000 1ffff 4743000a 6870796c 72616843 26 8f 71 0 1ffff 10000 0 10220000 5380 8f00 7100 0 1ffff00 1000000 0 44000000 3c8010 8f0000 710000 0 ffff0000 1 1 0 3580106f 8f000000 71000000 0 ff000000 1ff 100 0 80106e00 35 8f 71 0 1ffff 10000 0 10650000 2680 8f00 7100 0 1ffff00 1000000 0 22000000 0 0 ffff0000 140001 796c4743 69536870 656c706d 706d6f43 7265736f 0 0 1158 a66 0 1ffff 4743000a 6870796c 6d726554 1 8f ffffffff 0 1ffff 10000 0 0 0 0 60018 60000 60000 60000 0 2360000 cb0000 ffff0000 ffffffff ffffffff 1 1 0 0 0 1 0 3 454d4305 25453 de028000 20 0'33 10001 0 0 0 0 3601 0 10000 0 0 0 0 0d@@f(x) := sin(b*x)Times New Roman "Done"Times New Roman   ff ffffffff 1 1 0 0 0 1 0 3 454d4305 25453 de028000 20 10000'NANI(ť@dd;7 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0 1 0 ffff0004 f0001 796c4743 61506870 4c6e6572 37746665 8f000000 ff000000 ffffff 1000000 100 100 0 80092800 3d 8f 71 0 ffff 10000 0 10000 3d800b 8f0000 710000 0 ffff0000 0 1 0 ffff0002 80001 796c4743 494d6870 3c 8f 71 0 ffff 10000 0 10000 3c800b 8f0000 710000 0 ffff0000 0 1 0 80100001 3c 8f 71 0 10003 10000 0 780000 0 0 1300 ff000000 a0001ff 6c474300 54687079 16d7265 8f000000 ff000000 ffffff ff000000 1ff 100 0 0 0 13000000 1ffff00 43001000 70796c47 72615068 69526e65 37746867 8f000000 ff000000 ffffff 1000000 100 100 0 801f2900 1 8f ffffffff 0 1ffff 10000 0 0 0 0 10013 180000 190022 1ffff 47430008 6870796c 974f4d 8f0000 710000 0 ffff0000 1 1 0 800b0001 97 8f 71 0 ffff 10000 0 40000 1e8010 8f0000 710000 0 ffff0000 0 1 0 17801020 8f000000 71000000 0 ff000000 ff 100 0 80103a00 44 8f 71 0 ffff 10000 0 103d0000 1e80 8f00 7100 0 ffff00 1000000 0 20000000 0 0 0 0 79800d 8f0000 710000 0 ffff0000 0 1 0 800b0001 79 8f 71 0 ffff 10000 0 30000 2d8010 8f0000 710000 0 ffff0000 1 1 0 17801073 8f000000 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68 0 0 0 0 0 ff0000 ffff0000 7800ff 640000 53090000 49546474 646c6f42 1 1 30000 50004 70006 2360008 cb0000 710000 0 0 0 1 0 1ffff 4743000a 6870796c 4854414d 146 8f 71 0 ffff 10000 0 10000 1ffff 4743000a 6870796c 574f524d 146 8f 71 0 ffff 10000 0 20000 1ffff 47430008 6870796c 145534d 8f0000 710000 0 ffff0000 0 1 0 800b0001 145 8f 71 0 ffff 10000 0 60000 1ffff 4743000a 6870796c 72616843 26 8f 71 0 1ffff 10000 0 10220000 5380 8f00 7100 0 1ffff00 1000000 0 44000000 3c8010 8f0000 710000 0 ffff0000 1 1 0 3580106f 8f000000 71000000 0 ff000000 1ff 100 0 80106e00 35 8f 71 0 1ffff 10000 0 10650000 2680 8f00 7100 0 1ffff00 1000000 0 22000000 0 0 ffff0000 140001 796c4743 69536870 656c706d 706d6f43 7265736f 0 0 1158 a6e 0 1ffff 4743000a 6870796c 6d726554 1 8f ffffffff 0 1ffff 10000 0 0 0 0 60018 60000 60000 60000 0 2360000 cb0000 ffff0000 ffffffff ffffffff 1 1 0 0 0 1 0 3 454d4305 25453 de028000 20 10000'33 10001 0 0 0 0 3601 0 10000 0 0 0 0 0d@@f(x) := sin(x + c)Times New Roman "Done"Times New 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