0,10 m

0,15 m

0,05 m

0,20 m

0,25 m

0,30 m

0,60 m

0,80 m

0,35 m

0,40 m

0,45 m

0,50 m

0,55 m

0,65 m

0,70 m

0,75 m

0,85 m

Numerische Werte

{s_0\over m}

{T \over s}

T = T(s_0)

0

0,5

1,5

1,7

Harmonisch

Schwingung

Reale Schwingung

Version Stand
11.12.2021
Andreas Jäger

Stand

s0 = 0.2878352102738584 (slider from 0 to 0.85, step 0.05)
S0: (0, s0)
l: {(0, 0.05), (0.01, 0.0499554), (0.02, 0.0498219), (0.03, 0.0495997), (0.04, 0.0492892), (0.05, 0.0488908), (0.06, 0.0484054), (0.07, 0.0478338), (0.08, 0.047177), (0.09, 0.0464361), (0.1, 0.0456125), (0.11, 0.0447077), (0.12, 0.0437233), (0.13, 0.0426609), (0.14, 0.0415225), (0.15, 0.0403102), (0.16, 0.039026), (0.17, 0.0376723), (0.18, 0.0362515), (0.19, 0.0347661), (0.2, 0.0332187), (0.21, 0.0316121), (0.22, 0.0299491), (0.23, 0.0282328), (0.24, 0.0264661), (0.25, 0.0246523), (0.26, 0.0227945), (0.27, 0.0208961), (0.28, 0.0189604), (0.29, 0.0169909), (0.3, 0.0149911), (0.31, 0.0129646), (0.32, 0.010915), (0.33, 0.00884586), (0.34, 0.00676099), (0.35, 0.00466405), (0.36, 0.0025588), (0.37, 0.000448992), (0.38, -0.00166162), (0.39, -0.00376927), (0.4, -0.0058702), (0.41, -0.00796066), (0.42, -0.0100369), (0.43, -0.0120953), (0.44, -0.0141321), (0.45, -0.0161437), (0.46, -0.0181265), (0.47, -0.020077), (0.48, -0.0219917), (0.49, -0.0238672), (0.5, -0.0257001), (0.51, -0.0274872), (0.52, -0.0292253), (0.53, -0.0309114), (0.54, -0.0325423), (0.55, -0.0341152), (0.56, -0.0356273), (0.57, -0.037076), (0.58, -0.0384585), (0.59, -0.0397726), (0.6, -0.0410157), (0.61, -0.0421858), (0.62, -0.0432807), (0.63, -0.0442986), (0.64, -0.0452375), (0.65, -0.0460958), (0.66, -0.046872), (0.67, -0.0475647), (0.68, -0.0481727), (0.69, -0.0486949), (0.7, -0.0491304), (0.71, -0.0494784), (0.72, -0.0497382), (0.73, -0.0499095), (0.74, -0.0499919), (0.75, -0.0499852), (0.76, -0.0498896), (0.77, -0.0497051), (0.78, -0.049432), (0.79, -0.049071), (0.8, -0.0486225), (0.81, -0.0480874), (0.82, -0.0474667), (0.83, -0.0467615), (0.84, -0.0459729), (0.85, -0.0451025), (0.86, -0.0441517), (0.87, -0.0431222), (0.88, -0.042016), (0.89, -0.0408348), (0.9, -0.039581), (0.91, -0.0382566), (0.92, -0.036864), (0.93, -0.0354057), (0.94, -0.0338843), (0.95, -0.0323026), (0.96, -0.0306632), (0.97, -0.0289693), (0.98, -0.0272236), (0.99, -0.0254295), (1, -0.02359), (1.01, -0.0217084), (1.02, -0.0197882), (1.03, -0.0178326), (1.04, -0.0158453), (1.05, -0.0138297), (1.06, -0.0117895), (1.07, -0.00972821), (1.08, -0.00764959), (1.09, -0.00555733), (1.1, -0.00345516), (1.11, -0.00134683), (1.12, 0.000763903), (1.13, 0.00287327), (1.14, 0.00497752), (1.15, 0.00707289), (1.16, 0.00915565), (1.17, 0.0112221), (1.18, 0.0132685), (1.19, 0.0152913), (1.2, 0.0172867), (1.21, 0.0192514), (1.22, 0.0211818), (1.23, 0.0230743), (1.24, 0.0249258), (1.25, 0.0267328), (1.26, 0.0284921), (1.27, 0.0302007), (1.28, 0.0318554), (1.29, 0.0334534), (1.3, 0.0349917), (1.31, 0.0364676), (1.32, 0.0378786), (1.33, 0.0392221), (1.34, 0.0404957), (1.35, 0.0416971), (1.36, 0.0428243), (1.37, 0.0438751), (1.38, 0.0448478), (1.39, 0.0457406), (1.4, 0.0465519), (1.41, 0.0472803), (1.42, 0.0479245), (1.43, 0.0484833), (1.44, 0.0489558), (1.45, 0.0493411), (1.46, 0.0496385), (1.47, 0.0498475), (1.48, 0.0499677), (1.49, 0.0499989), (1.5, 0.0499411), (1.51, 0.0497944), (1.52, 0.049559), (1.53, 0.0492353), (1.54, 0.0488239), (1.55, 0.0483256), (1.56, 0.0477411), (1.57, 0.0470717), (1.58, 0.0463184), (1.59, 0.0454826), (1.6, 0.0445658), (1.61, 0.0435696), (1.62, 0.0424958), (1.63, 0.0413463), (1.64, 0.0401231), (1.65, 0.0388284), (1.66, 0.0374645), (1.67, 0.0360339), (1.68, 0.034539), (1.69, 0.0329826), (1.7, 0.0313674), (1.71, 0.0296963), (1.72, 0.0279723), (1.73, 0.0261984), (1.74, 0.0243778), (1.75, 0.0225137), (1.76, 0.0206095), (1.77, 0.0186686), (1.78, 0.0166944), (1.79, 0.0146904), (1.8, 0.0126602), (1.81, 0.0106074), (1.82, 0.0085357), (1.83, 0.00644879), (1.84, 0.00435038), (1.85, 0.00224422), (1.86, 0.000134045), (1.87, -0.00197636), (1.88, -0.00408325), (1.89, -0.00618285), (1.9, -0.00827143), (1.91, -0.0103453), (1.92, -0.0124006), (1.93, -0.0144339), (1.94, -0.0164414), (1.95, -0.0184196), (1.96, -0.020365), (1.97, -0.0222741), (1.98, -0.0241434), (1.99, -0.0259697), (2, -0.0277497), (2.01, -0.0294802), (2.02, -0.0311582), (2.03, -0.0327807), (2.04, -0.0343447), (2.05, -0.0358475), (2.06, -0.0372865), (2.07, -0.038659), (2.08, -0.0399626), (2.09, -0.041195), (2.1, -0.042354), (2.11, -0.0434375), (2.12, -0.0444437), (2.13, -0.0453706), (2.14, -0.0462168), (2.15, -0.0469806), (2.16, -0.0476608), (2.17, -0.0482561), (2.18, -0.0487654), (2.19, -0.0491878), (2.2, -0.0495227), (2.21, -0.0497694), (2.22, -0.0499274), (2.23, -0.0499965), (2.24, -0.0499766), (2.25, -0.0498676), (2.26, -0.0496699), (2.27, -0.0493837), (2.28, -0.0490095), (2.29, -0.0485481), (2.3, -0.0480002), (2.31, -0.0473668), (2.32, -0.046649), (2.33, -0.0458482), (2.34, -0.0449656), (2.35, -0.044003), (2.36, -0.042962), (2.37, -0.0418444), (2.38, -0.0406523), (2.39, -0.0393877), (2.4, -0.038053), (2.41, -0.0366505), (2.42, -0.0351826), (2.43, -0.0336521), (2.44, -0.0320615), (2.45, -0.0304139), (2.46, -0.028712), (2.47, -0.0269589), (2.48, -0.0251578), (2.49, -0.0233118), (2.5, -0.0214243), (2.51, -0.0194986), (2.52, -0.0175381), (2.53, -0.0155463), (2.54, -0.0135268), (2.55, -0.0114832), (2.56, -0.00941909), (2.57, -0.0073382), (2.58, -0.00524422), (2.59, -0.0031409), (2.6, -0.00103197), (2.61, 0.0010788), (2.62, 0.00318764), (2.63, 0.0052908), (2.64, 0.00738452), (2.65, 0.00946508), (2.66, 0.0115288), (2.67, 0.0135719), (2.68, 0.0155908), (2.69, 0.0175819), (2.7, 0.0195417), (2.71, 0.0214666), (2.72, 0.0233532), (2.73, 0.0251983), (2.74, 0.0269984), (2.75, 0.0287503), (2.76, 0.030451), (2.77, 0.0320975), (2.78, 0.0336867), (2.79, 0.0352159), (2.8, 0.0366823), (2.81, 0.0380834), (2.82, 0.0394166), (2.83, 0.0406795), (2.84, 0.04187), (2.85, 0.0429859), (2.86, 0.0440252), (2.87, 0.0449861), (2.88, 0.0458668), (2.89, 0.0466659), (2.9, 0.0473818), (2.91, 0.0480133), (2.92, 0.0485593), (2.93, 0.0490188), (2.94, 0.049391), (2.95, 0.0496752), (2.96, 0.049871), (2.97, 0.049978), (2.98, 0.0499959), (2.99, 0.0499248), (3, 0.0497649), (3.01, 0.0495162), (3.02, 0.0491794), (3.03, 0.048755), (3.04, 0.0482438), (3.05, 0.0476466), (3.06, 0.0469646), (3.07, 0.0461989), (3.08, 0.0453509), (3.09, 0.0444222), (3.1, 0.0434143), (3.11, 0.042329), (3.12, 0.0411684), (3.13, 0.0399344), (3.14, 0.0386292), (3.15, 0.0372552), (3.16, 0.0358148), (3.17, 0.0343106), (3.18, 0.0327453), (3.19, 0.0311216), (3.2, 0.0294424), (3.21, 0.0277107), (3.22, 0.0259296), (3.23, 0.0241024), (3.24, 0.0222321), (3.25, 0.0203222), (3.26, 0.0183761), (3.27, 0.0163972), (3.28, 0.014389), (3.29, 0.0123552), (3.3, 0.0102994), (3.31, 0.00822521), (3.32, 0.00613635), (3.33, 0.00403654), (3.34, 0.00192954), (3.35, -0.000180902), (3.36, -0.00229102), (3.37, -0.00439706), (3.38, -0.00649525), (3.39, -0.00858186), (3.4, -0.0106532), (3.41, -0.0127055), (3.42, -0.0147351), (3.43, -0.0167385), (3.44, -0.018712), (3.45, -0.0206522), (3.46, -0.0225555), (3.47, -0.0244187), (3.48, -0.0262383), (3.49, -0.0280111), (3.5, -0.029734), (3.51, -0.0314039), (3.52, -0.0330178), (3.53, -0.0345729), (3.54, -0.0360663), (3.55, -0.0374955), (3.56, -0.0388579), (3.57, -0.040151), (3.58, -0.0413726), (3.59, -0.0425204), (3.6, -0.0435925), (3.61, -0.044587), (3.62, -0.045502), (3.63, -0.046336), (3.64, -0.0470874), (3.65, -0.047755), (3.66, -0.0483375), (3.67, -0.0488339), (3.68, -0.0492434), (3.69, -0.0495651), (3.7, -0.0497986), (3.71, -0.0499433), (3.72, -0.0499992), (3.73, -0.0499659), (3.74, -0.0498437), (3.75, -0.0496328), (3.76, -0.0493334), (3.77, -0.0489462), (3.78, -0.0484718), (3.79, -0.0479111), (3.8, -0.047265), (3.81, -0.0465347), (3.82, -0.0457216), (3.83, -0.044827), (3.84, -0.0438526), (3.85, -0.0428), (3.86, -0.0416712), (3.87, -0.0404681), (3.88, -0.039193), (3.89, -0.037848), (3.9, -0.0364355), (3.91, -0.0349582), (3.92, -0.0334185), (3.93, -0.0318192), (3.94, -0.0301633), (3.95, -0.0284536), (3.96, -0.0266931), (3.97, -0.0248851), (3.98, -0.0230327), (3.99, -0.0211393), (4, -0.0192082), (4.01, -0.0172428), (4.02, -0.0152466), (4.03, -0.0132233), (4.04, -0.0111764), (4.05, -0.00910959), (4.06, -0.00702651), (4.07, -0.00493091), (4.08, -0.00282651), (4.09, -0.000717068), (4.1, 0.00139365), (4.11, 0.00350188), (4.12, 0.00560387), (4.13, 0.00769586), (4.14, 0.00977413), (4.15, 0.011835), (4.16, 0.0138747), (4.17, 0.0158897), (4.18, 0.0178764), (4.19, 0.0198312), (4.2, 0.0217506), (4.21, 0.0236312), (4.22, 0.0254697), (4.23, 0.0272629), (4.24, 0.0290074), (4.25, 0.0307002), (4.26, 0.0323383), (4.27, 0.0339187), (4.28, 0.0354387), (4.29, 0.0368955), (4.3, 0.0382866), (4.31, 0.0396095), (4.32, 0.0408618), (4.33, 0.0420413), (4.34, 0.0431459), (4.35, 0.0441736), (4.36, 0.0451226), (4.37, 0.0459912), (4.38, 0.046778), (4.39, 0.0474814), (4.4, 0.0481002), (4.41, 0.0486333), (4.42, 0.0490799), (4.43, 0.049439), (4.44, 0.0497101), (4.45, 0.0498926), (4.46, 0.0499863), (4.47, 0.049991), (4.48, 0.0499066), (4.49, 0.0497334), (4.5, 0.0494715), (4.51, 0.0491216), (4.52, 0.0486842), (4.53, 0.0481601), (4.54, 0.0475502), (4.55, 0.0468556), (4.56, 0.0460776), (4.57, 0.0452174), (4.58, 0.0442768), (4.59, 0.0432572), (4.6, 0.0421606), (4.61, 0.0409889), (4.62, 0.0397441), (4.63, 0.0384285), (4.64, 0.0370445), (4.65, 0.0355944), (4.66, 0.0340809), (4.67, 0.0325067), (4.68, 0.0308745), (4.69, 0.0291873), (4.7, 0.027448), (4.71, 0.0256599), (4.72, 0.023826), (4.73, 0.0219496), (4.74, 0.0200341), (4.75, 0.0180828), (4.76, 0.0160993), (4.77, 0.0140871), (4.78, 0.0120498), (4.79, 0.00999102), (4.8, 0.0079144), (4.81, 0.00582367), (4.82, 0.00372255), (4.83, 0.0016148), (4.84, -0.000495835), (4.85, -0.00260559), (4.86, -0.00471069), (4.87, -0.00680739), (4.88, -0.00889196), (4.89, -0.0109607), (4.9, -0.0130098), (4.91, -0.0150358), (4.92, -0.0170349), (4.93, -0.0190037), (4.94, -0.0209386), (4.95, -0.0228362), (4.96, -0.024693), (4.97, -0.0265058), (4.98, -0.0282714), (4.99, -0.0299866), (5, -0.0316483)}
x0 = 1.49 (slider from -5 to 5)
X0: (x0, 0)
w: (2 * π / x0)
f(x) = If[0 ≤ x ≤ x0, (s0 * cos((w * x)))]
l1 = Sequence(Segment[Element[l, i - 1], Element[l, i]], i, 2, Length[l])
c = Semicircle((0.55, 0), (-0.55, 0))
lx0: {1.49, 1.49, 1.49, 1.5, 1.51, 1.52, 1.53, 1.54, 1.55, 1.57, 1.59}
a = false
TTT: 1.48571 + (0.0398564 * s0) + (0.109907 * s0^(2)) + (0.294806 * s0^(3))
www: (2 * π / TTT)
g(x) = If[x ≥ 0, (s0 * cos((www * x)))]
gg(x) = If[0 ≤ x ≤ TTT, g(x)]
PTTT: (TTT, 0)
h(x) = If[1 ≤ x ≤ 1.9, 1.48571 + (0.03986 * (x - 1)) + (0.10991 * (x - 1)^(2)) + (0.29481 * (x - 1)^(3))] - 1.2
t: 0
PPTT: (s0 + 1, TTT - 1.2)
u = Vector((1, 0.29), (2, 0.29))
v = Vector((1, 0.29), (1, 0.7))
b = false
Text3: "\{" + (LaTeX[s0]) + "\ m\ \vert " + (LaTeX[TTT]) + "\ s\}"
d = false
fIdeal(x) = If[x ≥ 0, (s0 * cos((4.22908 * x)))]
Pe: ((1.5 * sin((www * t))), (0.55 * cos((www * t))))
Pe0: (0, (s0 * cos((www * t))))
PPe: (t, (s0 * cos((www * t))))
e = true
PPPel: ((1.5 * sin(((1.75 * s0) * cos((www * t))))), (-0.55 * cos(((1.75 * s0) * cos((www * t))))))
PPPPel: PPPel
i = Segment((0, 0), PPPel)
j = false