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Mr.Wizard
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P0h = 1.856*10^7;
 
V0h = .826063;
 
T0 = 299.817
 
g = 9.81;
 
Aac=.16;
 
Abe=.025;
 
Vr=1.067;
 
Vst=.006306;
 
Vh[x_] := Vr - x*Aac;
 
Vl[x_] := Vst + x*Abe;
 
m1 = 290000;
 
m4 = 9021;
 
k3 = 8*10^6;
 
R = 8.3144621;
 
Tc = 126.1;
 
Pc = 3.394*10^6;
 
\[Omega]ω = .040;
 
b = .07779607*(R*Tc)/Pc;
 
Trr[T_] := T/Tc;
 
\[Kappa]κ = .37464 + 1.54226 \[Omega]ω - .26993 \[Omega]^2
ω^2
\[Alpha][T_]α[T_] := (1 + \[Kappa]κ (1 - Sqrt[Trr[T]]))^2
 
ac = .45723553*(R^2*Tc^2)/Pc;
 
a[T_] := ac*\[Alpha][T]
ac*α[T]
nh = (P0h*V0h)/(R*T0);
 
nl = (P0l*V0l)/(R*T0);
 
Vmolh[x_] := Vh[x]/nh
 
Vmoll[x_] := Vl[x]/nl

Ppr[x_] := (R*T0)/(Vmolh[x] - b) - 
  a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)

Fpr[x_] := 
 Aac ((R*T0)/(Vmolh[x] - b) - 
     a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)) - 
  Abe ((R*T0)/(Vmoll[x] - b) - 
     a[T0]/(Vmoll[x]^2 + 2*b*Vmoll[x] - b^2))

A1 = .1;
 
ω2 = π/4;
 
c = 10000;
 
d = 300000;

ctipmot[t_] := A1 Cos[ω2 t]

prsol = NDSolve[{-c x4'[t] - 
     k3 ((m4 g + Fpr[54/39.3701])/k3 + ctipmot[t] + x4[t]) + 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m4 g == 
    m4 x4''[t], -c x1'[t] - d x1'[t]*Abs[x1'[t]] - 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m1 g == m1 x1''[t], x1[0] == 1,
    x4[0] == 0, x1'[0] == 0, x4'[0] == 0}, {x1[t], x4[t]}, {t, 0, 
   100}]
P0h = 1.856*10^7;
 
V0h = .826063;
 
T0 = 299.817
 
g = 9.81;
 
Aac=.16;
 
Abe=.025;
 
Vr=1.067;
 
Vst=.006306;
 
Vh[x_] := Vr - x*Aac;
 
Vl[x_] := Vst + x*Abe;
 
m1 = 290000;
 
m4 = 9021;
 
k3 = 8*10^6;
 
R = 8.3144621;
 
Tc = 126.1;
 
Pc = 3.394*10^6;
 
\[Omega] = .040;
 
b = .07779607*(R*Tc)/Pc;
 
Trr[T_] := T/Tc;
 
\[Kappa] = .37464 + 1.54226 \[Omega] - .26993 \[Omega]^2

\[Alpha][T_] := (1 + \[Kappa] (1 - Sqrt[Trr[T]]))^2
 
ac = .45723553*(R^2*Tc^2)/Pc;
 
a[T_] := ac*\[Alpha][T]

nh = (P0h*V0h)/(R*T0);
 
nl = (P0l*V0l)/(R*T0);
 
Vmolh[x_] := Vh[x]/nh
 
Vmoll[x_] := Vl[x]/nl

Ppr[x_] := (R*T0)/(Vmolh[x] - b) - 
  a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)

Fpr[x_] := 
 Aac ((R*T0)/(Vmolh[x] - b) - 
     a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)) - 
  Abe ((R*T0)/(Vmoll[x] - b) - 
     a[T0]/(Vmoll[x]^2 + 2*b*Vmoll[x] - b^2))

A1 = .1;
 
ω2 = π/4;
 
c = 10000;
 
d = 300000;

ctipmot[t_] := A1 Cos[ω2 t]

prsol = NDSolve[{-c x4'[t] - 
     k3 ((m4 g + Fpr[54/39.3701])/k3 + ctipmot[t] + x4[t]) + 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m4 g == 
    m4 x4''[t], -c x1'[t] - d x1'[t]*Abs[x1'[t]] - 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m1 g == m1 x1''[t], x1[0] == 1,
    x4[0] == 0, x1'[0] == 0, x4'[0] == 0}, {x1[t], x4[t]}, {t, 0, 
   100}]
P0h = 1.856*10^7;
V0h = .826063;
T0 = 299.817
g = 9.81;
Aac=.16;
Abe=.025;
Vr=1.067;
Vst=.006306;
Vh[x_] := Vr - x*Aac;
Vl[x_] := Vst + x*Abe;
m1 = 290000;
m4 = 9021;
k3 = 8*10^6;
R = 8.3144621;
Tc = 126.1;
Pc = 3.394*10^6;
ω = .040;
b = .07779607*(R*Tc)/Pc;
Trr[T_] := T/Tc;
κ = .37464 + 1.54226 ω - .26993 ω^2
α[T_] := (1 + κ (1 - Sqrt[Trr[T]]))^2
ac = .45723553*(R^2*Tc^2)/Pc;
a[T_] := ac*α[T]
nh = (P0h*V0h)/(R*T0);
nl = (P0l*V0l)/(R*T0);
Vmolh[x_] := Vh[x]/nh
Vmoll[x_] := Vl[x]/nl

Ppr[x_] := (R*T0)/(Vmolh[x] - b) - 
  a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)

Fpr[x_] := 
 Aac ((R*T0)/(Vmolh[x] - b) - 
     a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)) - 
  Abe ((R*T0)/(Vmoll[x] - b) - 
     a[T0]/(Vmoll[x]^2 + 2*b*Vmoll[x] - b^2))

A1 = .1;
ω2 = π/4;
c = 10000;
d = 300000;

ctipmot[t_] := A1 Cos[ω2 t]

prsol = NDSolve[{-c x4'[t] - 
     k3 ((m4 g + Fpr[54/39.3701])/k3 + ctipmot[t] + x4[t]) + 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m4 g == 
    m4 x4''[t], -c x1'[t] - d x1'[t]*Abs[x1'[t]] - 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m1 g == m1 x1''[t], x1[0] == 1,
    x4[0] == 0, x1'[0] == 0, x4'[0] == 0}, {x1[t], x4[t]}, {t, 0, 
   100}]
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matt
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P0h = 1.856*10^7;

V0h = .826063;

T0 = 299.817

g = 9.81;

Aac=.16;

Abe=.025;

Vr=1.067;

Vst=.006306;

Vh[x_] := Vr - x*Aac;

Vl[x_] := Vst + x*Abe;

m1 = 290000;

m4 = 9021;

k3 = 8*10^6;

R = 8.3144621;

Tc = 126.1;

Pc = 3.394*10^6;

\[Omega] = .040;

b = .07779607*(R*Tc)/Pc;

Trr[T_] := T/Tc;

\[Kappa] = .37464 + 1.54226 \[Omega] - .26993 \[Omega]^2

\[Alpha][T_] := (1 + \[Kappa] (1 - Sqrt[Trr[T]]))^2

ac = .45723553*(R^2*Tc^2)/Pc;

a[T_] := ac*\[Alpha][T]

nh = (P0h*V0h)/(R*T0);

nl = (P0l*V0l)/(R*T0);

Vmolh[x_] := Vh[x]/nh

Vmoll[x_] := Vl[x]/nl

Ppr[x_] := (R*T0)/(Vmolh[x] - b) - 
  a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)

Fpr[x_] := 
 Aac ((R*T0)/(Vmolh[x] - b) - 
     a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)) - 
  Abe ((R*T0)/(Vmoll[x] - b) - 
     a[T0]/(Vmoll[x]^2 + 2*b*Vmoll[x] - b^2))

A1 = .1;

ω2 = π/4;

c = 10000;

d = 300000;

ctipmot[t_] := A1 Cos[ω2 t]

prsol = NDSolve[{-c x4'[t] - 
     k3 ((m4 g + Fpr[54/39.3701])/k3 + ctipmot[t] + x4[t]) + 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m4 g == 
    m4 x4''[t], -c x1'[t] - d x1'[t]*Abs[x1'[t]] - 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m1 g == m1 x1''[t], x1[0] == 1,
    x4[0] == 0, x1'[0] == 0, x4'[0] == 0}, {x1[t], x4[t]}, {t, 0, 
   100}]
Aac=.16;

Abe=.025;

Vr=1.067;

Vst=.006306;

Vh[x_] := Vr - x*Aac;

Vl[x_] := Vst + x*Abe;

m1 = 290000;

m4 = 9021;

k3 = 8*10^6;

R = 8.3144621;

Tc = 126.1;

Pc = 3.394*10^6;

\[Omega] = .040;

b = .07779607*(R*Tc)/Pc;

Trr[T_] := T/Tc;

\[Kappa] = .37464 + 1.54226 \[Omega] - .26993 \[Omega]^2

\[Alpha][T_] := (1 + \[Kappa] (1 - Sqrt[Trr[T]]))^2

ac = .45723553*(R^2*Tc^2)/Pc;

a[T_] := ac*\[Alpha][T]

nh = (P0h*V0h)/(R*T0);

nl = (P0l*V0l)/(R*T0);

Vmolh[x_] := Vh[x]/nh

Vmoll[x_] := Vl[x]/nl

Ppr[x_] := (R*T0)/(Vmolh[x] - b) - 
  a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)

Fpr[x_] := 
 Aac ((R*T0)/(Vmolh[x] - b) - 
     a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)) - 
  Abe ((R*T0)/(Vmoll[x] - b) - 
     a[T0]/(Vmoll[x]^2 + 2*b*Vmoll[x] - b^2))

A1 = .1;

ω2 = π/4;

c = 10000;

d = 300000;

ctipmot[t_] := A1 Cos[ω2 t]

prsol = NDSolve[{-c x4'[t] - 
     k3 ((m4 g + Fpr[54/39.3701])/k3 + ctipmot[t] + x4[t]) + 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m4 g == 
    m4 x4''[t], -c x1'[t] - d x1'[t]*Abs[x1'[t]] - 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m1 g == m1 x1''[t], x1[0] == 1,
    x4[0] == 0, x1'[0] == 0, x4'[0] == 0}, {x1[t], x4[t]}, {t, 0, 
   100}]
P0h = 1.856*10^7;

V0h = .826063;

T0 = 299.817

g = 9.81;

Aac=.16;

Abe=.025;

Vr=1.067;

Vst=.006306;

Vh[x_] := Vr - x*Aac;

Vl[x_] := Vst + x*Abe;

m1 = 290000;

m4 = 9021;

k3 = 8*10^6;

R = 8.3144621;

Tc = 126.1;

Pc = 3.394*10^6;

\[Omega] = .040;

b = .07779607*(R*Tc)/Pc;

Trr[T_] := T/Tc;

\[Kappa] = .37464 + 1.54226 \[Omega] - .26993 \[Omega]^2

\[Alpha][T_] := (1 + \[Kappa] (1 - Sqrt[Trr[T]]))^2

ac = .45723553*(R^2*Tc^2)/Pc;

a[T_] := ac*\[Alpha][T]

nh = (P0h*V0h)/(R*T0);

nl = (P0l*V0l)/(R*T0);

Vmolh[x_] := Vh[x]/nh

Vmoll[x_] := Vl[x]/nl

Ppr[x_] := (R*T0)/(Vmolh[x] - b) - 
  a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)

Fpr[x_] := 
 Aac ((R*T0)/(Vmolh[x] - b) - 
     a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)) - 
  Abe ((R*T0)/(Vmoll[x] - b) - 
     a[T0]/(Vmoll[x]^2 + 2*b*Vmoll[x] - b^2))

A1 = .1;

ω2 = π/4;

c = 10000;

d = 300000;

ctipmot[t_] := A1 Cos[ω2 t]

prsol = NDSolve[{-c x4'[t] - 
     k3 ((m4 g + Fpr[54/39.3701])/k3 + ctipmot[t] + x4[t]) + 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m4 g == 
    m4 x4''[t], -c x1'[t] - d x1'[t]*Abs[x1'[t]] - 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m1 g == m1 x1''[t], x1[0] == 1,
    x4[0] == 0, x1'[0] == 0, x4'[0] == 0}, {x1[t], x4[t]}, {t, 0, 
   100}]
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matt
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Aac=.16;

Abe=.025;

Vr=1.067;

Vst=.006306;

Vh[x_] := Vr - x*Aac;

Vl[x_] := Vst + x*Abe;

m1 = 290000;

m4 = 9021;

k3 = 8*10^6;

R = 8.3144621;

Tc = 126.1;

Pc = 3.394*10^6;

\[Omega] = .040;

b = .07779607*(R*Tc)/Pc;

Trr[T_] := T/Tc;

\[Kappa] = .37464 + 1.54226 \[Omega] - .26993 \[Omega]^2

\[Alpha][T_] := (1 + \[Kappa] (1 - Sqrt[Trr[T]]))^2

ac = .45723553*(R^2*Tc^2)/Pc;

a[T_] := ac*\[Alpha][T]

nh = (P0h*V0h)/(R*T0);

nl = (P0l*V0l)/(R*T0);

Vmolh[x_] := Vh[x]/nh

Vmoll[x_] := Vl[x]/nl

Ppr[x_] := (R*T0)/(Vmolh[x] - b) - 
  a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)

Fpr[x_] := 
 Aac ((R*T0)/(Vmolh[x] - b) - 
     a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)) - 
  Abe ((R*T0)/(Vmoll[x] - b) - 
     a[T0]/(Vmoll[x]^2 + 2*b*Vmoll[x] - b^2))

A1 = .1;

ω2 = π/4;

c = 10000;

d = 300000;

ctipmot[t_] := A1 Cos[ω2 t]

prsol = NDSolve[{-c x4'[t] - 
     k3 ((m4 g + Fpr[54/39.3701])/k3 + ctipmot[t] + x4[t]) + 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m4 g == 
    m4 x4''[t], -c x1'[t] - d x1'[t]*Abs[x1'[t]] - 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m1 g == m1 x1''[t], x1[0] == 1,
    x4[0] == 0, x1'[0] == 0, x4'[0] == 0}, {x1[t], x4[t]}, {t, 0, 
   100}]
{x1[5]} instead of a value.

instead of a value.

A1 = .1;

ω2 = π/4;

c = 10000;

d = 300000;

ctipmot[t_] := A1 Cos[ω2 t]

prsol = NDSolve[{-c x4'[t] - 
     k3 ((m4 g + Fpr[54/39.3701])/k3 + ctipmot[t] + x4[t]) + 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m4 g == 
    m4 x4''[t], -c x1'[t] - d x1'[t]*Abs[x1'[t]] - 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m1 g == m1 x1''[t], x1[0] == 1,
    x4[0] == 0, x1'[0] == 0, x4'[0] == 0}, {x1[t], x4[t]}, {t, 0, 
   100}]
{x1[5]} instead of a value.
Aac=.16;

Abe=.025;

Vr=1.067;

Vst=.006306;

Vh[x_] := Vr - x*Aac;

Vl[x_] := Vst + x*Abe;

m1 = 290000;

m4 = 9021;

k3 = 8*10^6;

R = 8.3144621;

Tc = 126.1;

Pc = 3.394*10^6;

\[Omega] = .040;

b = .07779607*(R*Tc)/Pc;

Trr[T_] := T/Tc;

\[Kappa] = .37464 + 1.54226 \[Omega] - .26993 \[Omega]^2

\[Alpha][T_] := (1 + \[Kappa] (1 - Sqrt[Trr[T]]))^2

ac = .45723553*(R^2*Tc^2)/Pc;

a[T_] := ac*\[Alpha][T]

nh = (P0h*V0h)/(R*T0);

nl = (P0l*V0l)/(R*T0);

Vmolh[x_] := Vh[x]/nh

Vmoll[x_] := Vl[x]/nl

Ppr[x_] := (R*T0)/(Vmolh[x] - b) - 
  a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)

Fpr[x_] := 
 Aac ((R*T0)/(Vmolh[x] - b) - 
     a[T0]/(Vmolh[x]^2 + 2*b*Vmolh[x] - b^2)) - 
  Abe ((R*T0)/(Vmoll[x] - b) - 
     a[T0]/(Vmoll[x]^2 + 2*b*Vmoll[x] - b^2))

A1 = .1;

ω2 = π/4;

c = 10000;

d = 300000;

ctipmot[t_] := A1 Cos[ω2 t]

prsol = NDSolve[{-c x4'[t] - 
     k3 ((m4 g + Fpr[54/39.3701])/k3 + ctipmot[t] + x4[t]) + 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m4 g == 
    m4 x4''[t], -c x1'[t] - d x1'[t]*Abs[x1'[t]] - 
     Fpr[x1[t] - x4[t] + 54/39.3701] + m1 g == m1 x1''[t], x1[0] == 1,
    x4[0] == 0, x1'[0] == 0, x4'[0] == 0}, {x1[t], x4[t]}, {t, 0, 
   100}]
{x1[5]}

instead of a value.

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Dr. belisarius
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C. E.
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