x''+2δx'+ω_0^2x=0

A

A

A

Start

A

A

x(t)

x

y=x'

t

ω_0 = 1 (slider from 0 to 2, step 0.02)
δ = 0.1 (slider from -1 to 5, step 0.05)
xmin = -6 (slider from -10 to 15, step 1)
xmax = 10 (slider from -10 to 15, step 1)
ymin = -6 (slider from -10 to 15, step 1)
ymax = 6 (slider from -10 to 15, step 1)
mm = Sequence(Sequence[If[yy > 0, atan(((-ω_0^(2)) * xx / yy) - (2 * δ)), If[yy < 0, atan(((-ω_0^(2)) * xx / yy) - (2 * δ)) + π]], xx, xmin, xmax], yy, ymin, ymax)
rr = 0.09 (slider from -5 to 5, step 0.01)
phi = 0.7235987755982988
Start = (4.85, -6.1)
Dk: sqrt(δ^(2) - ω_0^(2))
ω_d: sqrt(ω_0^(2) - δ^(2))
C_1: (y(Start) + (δ * x(Start))) / ω_d
Ks = CurveCartesian((exp(((-δ) * t)) * ((C_1 * sin((ω_d * t))) + (x(Start) * cos((ω_d * t))))), (((-δ) * exp(((-δ) * t))) * ((C_1 * sin((ω_d * t))) + (x(Start) * cos((ω_d * t))))) + (exp(((-δ) * t)) * (((C_1 * ω_d) * cos((ω_d * t))) - ((x(Start) * ω_d) * sin((ω_d * t))))), t, 0, 50)
k_1: δ - Dk
k_2: δ + Dk
B_1: ((x(Start) * k_2) + y(Start)) / (k_2 - k_1)
B_2: ((x(Start) * k_1) + y(Start)) / (k_1 - k_2)
Kk = CurveCartesian((B_1 * exp(((-k_1) * t))) + (B_2 * exp(((-k_2) * t))), (((-k_1) * B_1) * exp(((-k_1) * t))) - ((k_2 * B_2) * exp(((-k_2) * t))), t, 0, 50)
A_1: y(Start) + (δ * x(Start))
Ka = CurveCartesian((((A_1 * t) + x(Start)) * exp(((-δ) * t))), (((-δ) * ((A_1 * t) + x(Start))) * exp(((-δ) * t))) + (A_1 * exp(((-δ) * t))), t, 0, 50)
fs(x) = If[0 ≤ x ≤ 50, (ℯ^(((-δ) * x)) * ((C_1 * sin((ω_d * x))) + (x(Start) * cos((ω_d * x)))))]
B = (-6, 5)
C = (-6, -5)
D = Point(xAxis)
E = Point(xAxis)
F = (-6, -5.5)
G = (-6, 5.76)
fk(x) = If[0 ≤ x ≤ 50, (B_1 * ℯ^(((-k_1) * x))) + (B_2 * ℯ^(((-k_2) * x)))]
t = 12.5 (slider from 0 to 17, step 0.1)
Ps: Ks(t)
Pa: Ka(t)
Pk: Kk(t)
ll = Sequence(Sequence[sqrt(yy^(2) + ((ω_0^(2) * xx) + ((2 * δ) * yy))^(2)), xx, xmin, xmax], yy, ymin, ymax)
Richtungsfeld = Sequence(Sequence[Vector[(i, j), (i + (((2 * rr) * Element[Element[ll, j - ymin + 1], i - xmin + 1]) * cos(Element[Element[mm, j - ymin + 1], i - xmin + 1])), j + (((2 * rr) * Element[Element[ll, j - ymin + 1], i - xmin + 1]) * sin(Element[Element[mm, j - ymin + 1], i - xmin + 1])))], i, xmin, xmax], j, ymin, ymax)
A: (t, x(Ks(t)))
H = (-3.82, 8.42)
I = (-3.82, 7.02)
J = (-0.64, 7.06)
K = (-0.66, 8.26)
FeldAchse = Sequence(Vector[(i, 0), (i, (((-2 * rr) * ω_0^(2)) * i))], i, -6, 12)
L = (4.32, 8.44)
M = (4.34, 6.9)
N = (8.74, 6.76)
O = (8.7, 8.4)
P: (0, fs(0))
Fs: (t, fs(t))
fa(x) = ((x(Start) + (y(Start) * x)) * ℯ^(((-δ) * x)))
Fk: (t, fk(t))
Fa: (t, fa(t))
Q = (26.40716979920645, -5.7507141931450905)
R = (37.53552255715046, -5.734868461981604)
S = (26.627890530913785, -3.777074010381327)