Modellieren periodischer Vorgänge
Wir haben uns jetzt längere Zeit mit der allgemeinen Sinusfunktion beschäftigt.
Bisher war das sehr unangewandt - das ändert sich jetzt - wir gehen also in die Realität und wollen periodische Vorgänge mathematisch beschreiben!
Füllt parallel bitte wieder das passende AB (Modellieren periodischer Vorgänge) auf Teams dazu aus!

Modellierung von Realsituationen
Bei den Aufnahmen ist der Sonnenstand in Abhängigkeit von der Tageszeit dargestellt.
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Modellierung periodischer Vorgänge
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Viele Vorgänge in der Natur wiederholen sich periodisch und können mit einer allgemeinen Sinusfunktion f mit modelliert werden. Dazu müssen die Parameter a, b, c und d so bestimmt werden, dass die Funktion den tatsächlichen Verlauf des Vorgangs ausreichend genau beschreibt.
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Bei der Modellierung durchlaufen wir 4 Schritte.
Diese wollen wir anhand des folgenden Beispiels genauer beleuchten:
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[/img]](https://www.geogebra.org/resource/fzfvxmgn/X20P8SWlqcEsFKjZ/material-fzfvxmgn.png)
Die Tageslänge, also die Zeit von Sonnenaufgang bis Sonnenuntergang, soll in Abhängigkeit von der Anzahl der Tage seit Jahresbeginn für Kempten für das Jahr 2021 auf der Grundlage der Daten obenstehender Tabelle modelliert werden.
Unser Ziel ist es, die Tageslänge für den 01. Mai 2021 im mathematischen Modell zu berechnen.
1. Schritt: Realsituation vereinfachen und idealisieren
Die verschiedenen Tageslängen kehren im Laufe der Jahre wieder. Somit liegt es nahe, die Tageslänge mit einer periodischen Funktion, speziell der Sinusfunktion, zu modellieren:
Wir benötigen gewisse Vereinfachungen für unser mathematisches Modell.
So gehen wir davon aus, dass die maximalen und minimalen Tageslängen jeweils immer gleich sind .
Auch die Periodenlänge sollten wir vereinfachen:
Wie könnte eine sinnvolle Periodenlänge in Tagen lauten?
Mithilfe dieser Vereinfachungen können wir dann zum zweiten Schritt übergehen.
2. Schritt: Ein mathematisches Modell erstellen
Man legt ein geeignetes Koordinatensystem fest, trägt die entsprechenden Punkte ein und skizziert dann eine Sinusfunktion durch diese Punkte. Unsere Aufgabe besteht dann darin, die Formel für die allgemeine Sinusfunktion anhand der gegebenen Werte herauszufinden.
Versuche vorerst obige allgemeine Sinusfunktion bestmöglich durch die vorgegebenen Punkte A-D laufen zu lassen, indem du die Schieberegler verwendest) und schreibe anschließend die einzelnen Parameter a, b, c und d auf:
Die einzelnen Parameter lauten laut Skizze:
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Wir wollen das Ganze jetzt ein wenig formaler berechnen und weniger durch Probieren mithilfe von GeoGebra. Dazu widmen wir uns jedem einzelnen Parameter der Reihe nach:
Der Parameter a gibt uns immer die Amplitude an. Diese finden wir heraus, indem wir uns den höchsten Wert (also den maximalen y-Wert) und den niedrigsten Wert (also den minimalen y-Wert) näher anschauen. Finden wir nämlich "den Abstand" zwischen diesen beiden Werten heraus und halbieren diesen, bekommen wir automatisch die Amplitude.
(Beispiel: Die normale Sinusfunktion hat den Abstand 2 zwischen höchsten und niedrigsten y-Wert. Halbieren wir diesen Wert kommen wir auf die Amplitude 1 und somit a = 1)
Eine allgemeine Formel zur Bestimmung von a könnte also wie folgt aussehen:
Da und gilt, können wir somit für a folgenden Wert berechnen:
Für den Parameter b ist die Periodenlänge entscheidend. Diese haben wir auf 365 (Tage) vereinfacht und können damit unser b berechnen.
Allgemein gilt:
Periodenlänge =
Da wir die Periodenlänge mit 365 Tagen bereits haben, können wir nach b umformen:
b ist also:
Um den Parameter c zu berechnen ist es sinnvoll vorerst den Parameter d zu betrachten.
Den Parameter d erhalten wir, indem wir den Mittelwert zwischen dem höchsten und niedrigsten y Wert ermitteln.
Eine allgemeine Formel zur Bestimmung von d könnte also wie folgt aussehen:
Für unser konkretes d ergibt sich also:
Hiermit können wir unsere Verschiebung und den Parameter c ermitteln.
Wir müssen einen Tag finden, an dem wir diesen Wert von d annehmen und an den folgenden Tagen im Graphen der Funktion steigen.
Ein möglicher Tag wäre also:
Dies ist umgerechnet seit Jahresbeginn (also 01.01.2021) der 79. Tag im Jahr.
Damit ergibt sich für die Verschiebung in x-Richtung:
Für unsere allgemeine Sinusfunktion können wir also folgende Funktionsgleichung annehmen:
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3. Schritt: Im mathematisches Modell arbeiten
Nun können wir unsere Grundfrage - nämlich die Berechnung der Tageslänge am 01. Mai in Kempten - im mathematischen Modell beantworten.
Der 01. Mai ist der 121. Tag im Jahr und damit können wir f(121) berechnen:
f(121) =
4. Schritt: Überprüfen der Ergebnisse an der Realsituation
Im Jahr betrug die tatsächlich gemessene Tageslänge am 1. Mai in Kempten 14,5 Stunden. Vergleicht man weitere tatsächlich gemessene Tageslängen mit den berechneten Werten, so zeigt sich, dass der Vorgang durch die Funktion gut angenähert wird.
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Damit habt hier die Theorie für heute geschafft!
An sich gar nicht so viel Neues, oder?
Jetzt wollen wir das "neue" Thema noch üben.
Bearbeitet dazu im Buch die Aufgaben:
B.S. 86/1
B.S. 87 / 5a.