Date: 4 Říjen 2013

φ_{01}

φ_{02}

ω_1t

φ_{01}

φ_{02}

$Δφ$

t_{02}

t_{01}

y_1 = y_{m1} \sin (φ_1)

y_2 = y_{m2} \sin(φ_{2} )

φ_1 = ω_1 t + φ_{01} 

φ_2 = ω_2 t + φ_{02} 

φ_{0} - \text{počáteční fáze 

φ - \text{fáze 

Δφ - \text{fázový rozdíl

Δφ = |φ_2 - φ_1| = |(ω_2 t + φ_{02}) - (ω_1 t + φ_{01})|

\text{pro izochronní kmity }(ω_1 = ω_2):

Δφ =  | φ_{02} - φ_{01}| = konst

\text{pro neizochronní kmity }(ω_1 ≠ ω_2):

Δφ =  | (ω_2 - ω_1) t  + φ_{02} - φ_{01}| ≠ konst

zobrazit vzorce

\omega_1=1

$Δφ$

čas nastavuj ručně:

φ02 = 1.30899693 (slider from 1.04719755 to 1.57079633, step 0.13089969)
ω2 = 1 (slider from 1 to 2, step 1)
ym2 = 2.4 (slider from 0 to 5, step 0.1)
φ01 = 0.26179938 (slider from 0 to 0.78539816, step 0.13089969)
ω1 = 1 (slider from 1 to 3, step 0.1)
ym1 = 1.6 (slider from 0 to 5, step 0.1)
f(x) = ym1 * sin(ω1 * x + φ01)
g(x) = ym2 * sin(ω2 * x + φ02)
t01: φ01 / ω1
t02: φ02 / ω2
h = Function(f, -t01, 0)
p = Function(g, -t02, 0)
q = Function(f, 0, 7)
r = Function(g, 0, 7)
a = Segment((0, 0), (-1 * t01, 0))
b = Segment((0, -0.1), (-1 * t02, -1 * 0.1))
A = (-4, 0)
c = Circle(A, ym1)
d = Circle(A, ym2)
B = Intersect(c, xAxis, 2)
C = Intersect(d, xAxis, 2)
B' = Rotate(B, φ01, A)
α = Angle(B, A, B')
u = Vector(A, B')
D: (0, f(0))
e = Segment(B', D)
C' = Rotate(C, φ02, A)
β = Angle(C, A, C')
v = Vector(A, C')
E: (0, g(0))
i = Segment(C', E)
t = 0 (slider from 0 to 2 * π / ω1, step 0.0010)
φ1: ω1 * t + φ01
φ2: ω2 * t + φ02
B'' = Rotate(B', ω1 * t, A)
γ = Angle(B', A, B'')
w = Vector(A, B'')
C'' = Rotate(C', ω2 * t, A)
δ = Angle(C', A, C'')
z = Vector(A, C'')
k = CircleArc(A, B, B')
F = Intersect(c, k, 1)
G = Midpoint(B', F)
H = Midpoint(C', C)
j = Ray(A, H)
I = Intersect(d, j, 1)
s = CircleArc(A, C, C')
ε = Angle(B'', A, C'')
l = Ray(A, G)
J = Intersect(k, l)
m = Segment((-1 * t02, -1 * 0.5), (-1 * t02, -1 * 0.1))
n = Segment((0, -0.5), (0, -0.1))
b_1 = Segment((0, -0.45), (-1 * t02, -1 * 0.45))
K: ((0, -1 * 0.45) + (-1 * t02, -1 * 0.45)) / 2
L = Intersect(b_1, m)
M = Intersect(b_1, n)
u_1 = Vector(K, L)
v_1 = Vector(K, M)
a_1 = Segment((-1 * t01, 0), (-1 * t01, 0))
c_1 = Segment((-1 * t01, 0), (-1 * t01, 0))
d_1 = Segment((-1 * t01, 0), (-1 * t01, -1 * 0.85))
e_1 = Segment((0, 0), (0, -0.85))
f_1 = Segment((-1 * t01, -1 * 0.8), (0, -0.8))
N: ((-1 * t01, -1 * 0.8) + (0, -1 * 0.8)) / 2
O = Intersect(d_1, f_1)
P = Intersect(f_1, e_1)
w_1 = Vector(N, O)
z_1 = Vector(N, P)
Q = (0.3875109158160687, -1.0535582065321112)
R = (4.3318198688153835, -1.0443640131684768)
o = false
ζ = Angle(B'', A, C'')
text19: "φ_{02}=" + (LaTeX[φ02 * 180 / π]) + "°"
text20: "φ_{01}=" + (LaTeX[φ01 * 180 / π]) + "°"
S: (t, g(t))
T: (t, f(t))
Δφ: abs((ω2 - ω1) * t + φ02 - φ01)
text21: "Δφ=" + (LaTeX[Δφ * 180 / π]) + "°"
text22: "Δφ= " + (LaTeX[Δφ * 180 / π]) + "°"