φ(t)

Dr. Markus Ziegler
CC BY-SA 3.0

a

v

s

s_{0} = 4.51 (slider from 1.2 to 5, step 0.01)
φ_{0} = 0 (slider from 0 to 1.999, step 0.001)
f = 0.124 (slider from 0.05 to 0.25, step 0.001)
omega: ((2 * π) * f)
t = 11.192 (slider from 0 to 26, step 0.001)
xKreismittelpunkt: -8
P_0: (xKreismittelpunkt, 0)
NullVektor = Vector(P_0, (0, 0))
φ: (((2 * π) * f) * t) + (φ_{0} * π)
zP_1: (s_{0} * ℯ^((ί * φ)))
zPunkt_1: zP_1 + P_0
s(x) = If[0 ≤ x ≤ t, (s_{0} * sin((omega * x) + (φ_{0} * π)))]
z_1 = Vector(P_0, zPunkt_1)
SKreis = Circle(P_0, zPunkt_1)
P_1: (t, s(t))
Verbindung_1 = Segment(P_1, zPunkt_1)
Winkelφ = Angle(NullVektor, z_1)
φd: Winkelφ / (180°)
Nullgerade = Segment((0, 0), ((2 * xKreismittelpunkt), 0))
Senkrechte = Segment((xKreismittelpunkt, -5), (xKreismittelpunkt, 5))
SchwerpunktKoerper: (-1.5, s(t))
Text1: " " + (LaTeX[φ_{0}]) + " \; π"
Text4: " " + (LaTeX[f]) + " \;Hz"
Text2: "" + (LaTeX[s_{0}]) + " \,cm"
Text5: "s(t)=s_0 \cdot \sin(\varphi(t)) = " + (LaTeX[s(t)]) + " \;cm "
Text7: "\\\varphi(t)=2\pi\cdot f\cdot t+\varphi_0=\omega\cdot t+\varphi_0 =  " + (LaTeX[φd]) + " \; \pi"
Text3: "" + (LaTeX[t]) + " \;s"
v(x) = If[0 ≤ x ≤ t, ((s_{0} * omega) * cos((omega * x) + (φ_{0} * π)))]
a(x) = If[0 ≤ x ≤ t, (((-s_{0}) * omega^(2)) * sin((((2 * π) * f) * x) + (φ_{0} * π)))]
zP_2: ((s_{0} * omega) * ℯ^((ί * (φ + π / 2))))
zP_3: ((s_{0} * omega^(2)) * ℯ^((ί * (φ + π))))
zPunkt_2: zP_2 + P_0
z_2 = Vector(P_0, zPunkt_2)
zPunkt_3: zP_3 + P_0
z_3 = Vector(P_0, zPunkt_3)
P_2: (t, v(t))
P_3: (t, a(t))
Verbindung_2 = Segment(P_2, zPunkt_2)
Verbindung_3 = Segment(P_3, zPunkt_3)
aAnzeige = true
vAnzeige = true
sAnzeige = true
Text8: "v(t)=s_0 \cdot \omega\cdot \cos(\varphi(t)) =  " + (LaTeX[v(t)]) + " \;{cm}/{s} "
Text9: "a(t)=-s_0 \cdot\omega^2\cdot \sin(\varphi(t)) =   " + (LaTeX[a(t)]) + " \;{cm}/{s^2} "
vKreis = Circle(P_0, zPunkt_2)
aKreis = Circle(P_0, zPunkt_3)
Winkelsv = Angle(z_1, z_2)
Winkelva = Angle(z_2, z_3)