Allgemeine Sinusfunktion
Author: Andreas Jäger
Date: 18 April 2013

f(x)=a + b x

f(x)=a + b x + c x²

f(x)=a + b x + c x² + d x³

f(x)=0

0

Stahlfeder

korrigiert

P_2 =

P_0 =

P_3 =

P_1 =

P_4 =

P_5 =

P_6 =

P_7 =

P_8 =

Zu

Auswertung \ von \ \sqrt{m}-T-Diagrammen

Version Stand
25.10.2019
Andreas Jäger

Stand

D(l)

GeoGebra-Arbeitsblatt zu “Praktikum-02-Federhärte”

korrigiert

m_0 =

f(x) = b x

0 g

7 g

16 g

m0 = 0 (slider from 0 to 0.02, step 0.00010)
x2 = 0.3308731105009209
x1 = 0.16315250935265246
xMax = Max(x1, x2)
xMin = Min(x1, x2)
dx: (xMax - xMin) / 2
P3: (sqrt(0.06 + m0), 0.81)
b3: xMin ≤ x(P3) ≤ xMax
P8: (-0.005, 0)
b8: xMin ≤ x(P8) ≤ xMax
P7: (sqrt(0.1 + m0), 1.01)
b7: xMin ≤ x(P7) ≤ xMax
P6: (sqrt(0.09 + m0), 0.97)
b6: xMin ≤ x(P6) ≤ xMax
P5: (sqrt(0.08 + m0), 0.91)
b5: xMin ≤ x(P5) ≤ xMax
P4: (sqrt(0.07 + m0), 0.86)
b4: xMin ≤ x(P4) ≤ xMax
P2: (sqrt(0.05 + m0), 0.73)
b2: xMin ≤ x(P2) ≤ xMax
n2 = If(b8, 9, If[b7, 8, If[b6, 7, If[b5, 6, If[b4, 5, If[b3, 4, If[b2, 3, 2]]]]]])
P1: (sqrt(0.04 + m0), 0.68)
b1: xMin ≤ x(P1) ≤ xMax
P0: (sqrt(0.03 + m0), 0.59)
PL: {P0, P1, P2, P3, P4, P5, P6, P7, P8}
b0: xMin ≤ x(P0) ≤ xMax
n1 = If(b0, 1, If[b1, 2, If[b2, 3, If[b3, 4, If[b4, 5, If[b5, 6, If[b6, 7, If[b7, 8, 8]]]]]]])
nn2 = Max(n1, n2)
nn1 = Min(n1, n2)
LL = Take(PL, nn1, nn2)
f1 = Fit(LL, {1, x})
P10 = NaN
f2 = Fit(LL, {1, x, x^(2)})
f3 = Fit(LL, {1, x, x^(2), x^(3)})
bf1: true
bf2: false
bf3: false
grad: 1
Eingabefeld1 = Textfield(P2)
be2: false
be0: false
be3: false
be4: false
be5: false
be6: false
be7: false
be8: false
Eingabefeld2 = Textfield(P0)
Eingabefeld3 = Textfield(P3)
Eingabefeld4 = Textfield(P1)
Eingabefeld5 = Textfield(P4)
Eingabefeld6 = Textfield(P5)
Eingabefeld7 = Textfield(P6)
Eingabefeld8 = Textfield(P7)
Eingabefeld9 = Textfield(P8)
be1: false
X1: (x1, 0)
X2: (x2, 0)
f = Ray(X1, X1 + (0, 3))
g = Ray(X2, X2 + (0, 3))
a = false
bd: false
b = Max(y(PL))
maxy = Max(y(PL))
faktor = -1 (slider from -2 to 2, step 1)
fak: 10^(faktor)
q(x) = (fak * f1'(x))
h(x) = (fak * f3'(x))
p(x) = (fak * f2'(x))
korr: sqrt(Sum[(y(LL) - f1(x(LL)))^(2)] / Length[LL])
Eingabefeld10 = Textfield(m0)
Text1: "C = {\Delta T\over \Delta \sqrt{m}} = " + (LaTeX[Slope[f1]]) + "\ {s \over \sqrt{kg}}\cr
D = {4\pi^2\over C^2} = " + (LaTeX[((4 * π^(2))) / Slope[f1]^(2)]) + "\cr"
f11 = Fit(LL, {x})
Text5: "C = {\Delta T\over \Delta \sqrt{m}} =  " + (LaTeX[Slope[f11]]) + " \ {s \over \sqrt{kg}}\cr
D = {4\pi^2\over C^2} = " + (LaTeX[((4 * π^(2))) / Slope[f11]^(2)]) + " \cr"
bf11: false
Abst = Sequence(y(Element[PL, i]) - f11(x(Element[PL, i])), i, 1, 8)
c = Sum(Abst^(2))
Text6 = LaTeX(c, true, true)
A: (sqrt(m0), (100 * c))