amortiguamiento de coulomb
Post on 12-Apr-2016
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DESCRIPTION
TRANSCRIPT
Datos
m = 3.0;
k = 1000;
Μ = 0.5;
g = 9.81;
x0 = 0.1;
v0 = 1;
t0 = 0;
Ecuaciones
Ωn =
k
m
Τ =
2 Π
Ωn
Primer Sección
Sol1 = DSolve@8m x''@tD + k x@tD -Μ m g, x@t0D x0, x'@t0D v0<, x@tD, tD
x01t = x@tD . Sol1@@1DD
PlotB:x01t, -
Μ g m
k
>, 8t, 0, Τ<, PlotStyle ® 8Blue, 8Blue, Dashed<<F
v01t = D@x01t, tDSol11 = FindRoot@v01t 0, 8t, 0<Dt1 = Re@tD . Sol11@@1DDx1 = Re@x01tD . t ® t1
Segunda Sección
Sol2 = DSolve@8m x''@tD + k x@tD +Μ m g, x@t1D x1, x'@t1D 0<, x@tD, tDx12t = x@tD . Sol2@@1DDPlot@x12t, 8t, 0, Τ<D
PlotB:x01t, x12t, +
Μ g m
k
>, 8t, 0, Τ<,
PlotStyle ® 8Blue, 8Red, Dashed<, 8Red, Dashed<<F
v12t = D@x12t, tD
Sol21 = FindRootBv12t 0, :t, t1 +
Τ
2
>F
t2 = t . Sol21@@1DDx2 = x12t . t ® t2
Tercera Sección
Sol3 = DSolve@8m x''@tD + k x@tD -Μ m g, x@t2D x2, x'@t2D 0<, x@tD, tDx23t = x@tD . Sol3@@1DDPlot@x23t, 8t, 0, Τ<D
PlotB:x01t, x12t, x23t, -
Μ g m
k
>, 8t, 0, Τ<,
PlotStyle ® 8Blue, Red, 8Green, Dashed<, 8Green, Dashed<<F
v23t = D@x23t, tD
Sol31 = FindRootBv23t 0, :t, t2 +
Τ
2
>F
t3 = Re@tD . Sol31@@1DDx3 = Re@x23tD . t ® t3
Cuarta Sección
Sol4 = DSolve@8m x''@tD + k x@tD +Μ m g, x@t3D x3, x'@t3D 0<, x@tD, tDx34t = x@tD . Sol4@@1DD
PlotB:x01t, x12t, x23t, x34t,Μ g m
k
>, 8t, 0, 2 Τ<,
PlotStyle ® 8Blue, Red, Green, 8Magenta, Dashed<, 8Magenta, Dashed<<F
v34t = D@x34t, tD
Sol41 = FindRootBv34t 0, :t, t3 +
Τ
2
>F
t4 = Re@tD . Sol41@@1DDx4 = Re@x34tD . t ® t4
Quinta Sección
Sol5 = DSolve@8m x''@tD + k x@tD -Μ m g, x@t4D x4, x'@t4D 0<, x@tD, tDx45t = x@tD . Sol5@@1DD
PlotB:x01t, x12t, x23t, x34t, x45t, -
Μ g m
k
>, 8t, 0, 2 Τ<,
PlotStyle ® 8Blue, Red, Green, Magenta, 8Blue, Dashed<, 8Blue, Dashed<<F
v45t = D@x45t, tD
Sol51 = FindRootBv45t 0, :t, t4 +
Τ
2
>F
t5 = Re@tD . Sol51@@1DDx5 = Re@x45tD . t ® t4
Gráfica
2 Amortiguamiento de Coulomb.nb
Gráfica
xTot = Piecewise@88x01t, t < t1<, 8x12t, t < t2<, 8x23t, t < t3<, 8x34t, t < t4<, 8x45t, t < t5<<D
PlotB:xTot,Μ m g
k
, -
Μ m g
k
>, 8t, 0, 3 Τ<, PlotRange ® All,
AxesLabel ® 8"t", "x@mD"<, PlotLabel ® "Amortiguamiento de Coulomb"F
Envolventes
t1
x1
m1 =
-2Μ m g
k
Τ
2
Sol6 = FindRoot@v12t m1, 8t, t1<Dtenv = t . Sol6@@1DDxenv = x12t . t -> tenv
xEnv1 = m1 Ht - tenvL + xenv
xEnv2 = -xEnv1
PlotB:xTot,Μ m g
k
, -
Μ m g
k
, xEnv1, xEnv2>, 8t, 0, 3 Τ<, PlotRange ® All,
AxesLabel ® 8"t", "x@mD"<, PlotLabel ® "Amortiguamiento de Coulomb"F
Amortiguamiento de Coulomb.nb 3
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