φ_2

Schwingung 2

Schwingung 1

Summe

φ_1

φ_{ges}

f_{ges} - (f_1+f_2)/2

Dr. Markus Ziegller 
CC BY-SA 3.0

P_0: (-11, 0)
NullVektor = Vector(P_0, (0, 0))
t = 40.81 (slider from 0 to t_{max}, step 1.0E-5)
s_{02} = 4 (slider from 0 to 5, step 0.1)
φ_{02} = 1.5 (slider from 0 to 1.999, step 0.1)
f_{2} = 482 (slider from 200 to 600, step 1)
φ_{2}: (((2 * π) * f_{2} / 1000) * t) + (φ_{02} * π)
zP_2: (s_{02} * ℯ^((ί * φ_{2})))
zPunkt_2: zP_2 + P_0
z_2 = Vector(P_0, zPunkt_2)
Winkelφ_2 = Angle(NullVektor, z_2)
f_{1} = 460 (slider from 200 to 600, step 1)
φ_{01} = 1.1 (slider from 0 to 1.999, step 0.1)
s_{01} = 4.2 (slider from 0 to 5, step 0.1)
φ_{1}: (((2 * π) * f_{1} / 1000) * t) + (φ_{01} * π)
Kurve_2 = true
Kurve_1 = true
zP_1: (s_{01} * ℯ^((ί * φ_{1})))
zPunkt_1: zP_1 + P_0
z_1 = Vector(P_0, zPunkt_1)
zP_{ges}: zP_1 + zP_2
zPunkt_{ges}: zPunkt_1 + zPunkt_2 - P_0
z_{ges} = Vector(P_0, zPunkt_{ges})
t_{max} = 106 (slider from 20 to 200, step 1)
s_{1}(x) = If[0 ≤ x ≤ t, (s_{01} * sin((((2 * π) * f_{1}) * x / 1000) + (φ_{01} * π)))]
s_{2}(x) = If[0 ≤ x ≤ t, (s_{02} * sin((((2 * π) * f_{2}) * x / 1000) + (φ_{02} * π)))]
s_{ges}(x) = s_{1}(x) + s_{2}(x)
Vekparallel_1 = Segment(zPunkt_1, zPunkt_{ges})
Vekparallel_2 = Segment(zPunkt_2, zPunkt_{ges})
c = Circle(P_0, zPunkt_1)
P_{ges}: (t, s_{ges}(t))
Verbindung_{ges} = Segment(P_{ges}, zPunkt_{ges})
P_1: (t, s_{1}(t))
P_2: (t, s_{2}(t))
Verbindung_1 = Segment(P_1, zPunkt_1)
Verbindung_2 = Segment(P_2, zPunkt_2)
d = Circle(P_0, zPunkt_2)
Kurve_{ges} = true
Winkelφ_1 = Angle(NullVektor, z_1)
φ2d: Winkelφ_2 / (180°)
φ1d: Winkelφ_1 / (180°)
φgesd: Angle[z_{ges}] / (180°)
Winkelφ_{ges} = Angle(NullVektor, z_{ges})
Nullgerade = Segment((0, 0), (-22, 0))
Senkrechte = Segment((-11, -5), (-11, 5))
Text1: "\varphi_1= " + (LaTeX[φ1d]) + " \;π"
Text3: "φ_2 =  " + (LaTeX[φ2d]) + " \;π"
Text6: "φ_{ges} = " + (LaTeX[φgesd]) + " \;π"
Text2: "" + (LaTeX[φ_{01}]) + "\;π"
Text7: "" + (LaTeX[φ_{02}]) + "\;π"
Text5: " " + (LaTeX[f_{2}]) + " \;Hz"
Text4: " " + (LaTeX[f_{1}]) + "\; Hz"
Text8: "" + (LaTeX[s_{01}]) + "\; mm"
Text9: "" + (LaTeX[s_{02}]) + "\; mm"
s1t: imaginary(zP_1)
s2t: imaginary(zP_2)
Text12: "s_2=" + (LaTeX[s2t]) + "\; mm"
Text11: "s_1=" + (LaTeX[s1t]) + "\; mm"
sgest: imaginary(zP_{ges})
Text13: "s_{ges}=" + (LaTeX[sgest]) + "\; mm"
Text10: "t=" + (LaTeX[t]) + "\; ms"
Δfges(x) = If[0 ≤ x ≤ t, ((f_{1} * s_{01}^(2)) + (f_{2} * s_{02}^(2)) + (((s_{01} * s_{02}) * (f_{1} + f_{2})) * cos((((2 * π) * (f_{1} - f_{2})) * x / 1000) + (π * (φ_{01} - φ_{02}))))) / (s_{01}^(2) + s_{02}^(2) + (((2 * s_{01}) * s_{02}) * cos((((2 * π) * (f_{1} - f_{2})) * x / 1000) + (π * (φ_{01} - φ_{02}))))) - (f_{1} + f_{2}) / 2]
KurveΔfges = false
Δfgest: Δfges(t)
Text14: "f_{ges}-(f_1+f_2)/2 = " + (LaTeX[Δfgest]) + "\; Hz"