Phase Curve

Author

Eric W. Weisstein
February 28, 2011

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DifferentialEquations/PhaseCurve.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PhaseCurve.html.

©2011 Wolfram Research, Inc. except for portions noted otherwise

Plots

V5

<<Graphics`Colors`
<<Typesetting`

Show[GraphicsArray[
{
ParametricPlot[Evaluate[{x[t],y[t]}/.DSolve[{x'[t]==y[t],y'[t]==-10x[t]-y[t],x[0]==1,y[0]==0},{x[t],y[t]},t][[1]]],{t,0,8},PlotRange->All,PlotStyle->Red,
AxesLabel->TraditionalForm/@{x,""},DisplayFunction->Identity,
PlotLabel->Style["damped harmonic oscillator",Italic]],
ParametricPlot[Evaluate[{x[t],y[t]}/.DSolve[{x'[t]==y[t],y'[t]==-10x[t],x[0]==1,y[0]==0},{x[t],y[t]},t][[1]]],{t,0,2},PlotRange->All,PlotStyle->Red,
DisplayFunction->Identity,
AxesLabel->TraditionalForm/@{x,""},PlotLabel->Style["simple harmonic oscillator",Italic]],
ParametricPlot[Evaluate[{x[t],y[t]}/.NDSolve[{x'[t]==y[t],y'[t]==-.26Sin[x[t]],x[0]==0,y[0]==1},{x[t],y[t]},{t,0,30}][[1]]],{t,0,30},PlotRange->All,PlotStyle->Red,
DisplayFunction->Identity,
AxesLabel->TraditionalForm/@{x,""},PlotLabel->Style["pendulum",Italic]]
}]]

V6

GraphicsRow[
{
ParametricPlot[Evaluate[{x[t],y[t]}/.DSolve[{x'[t]==y[t],y'[t]==-10x[t]-y[t],x[0]==1,y[0]==0},{x[t],y[t]},t][[1]]],{t,0,8},PlotRange->All,PlotStyle->Red,AspectRatio->1,
AxesLabel->{x,""},
PlotLabel->TextCell[Style["damped harmonic oscillator",Italic],PageWidth->100,TextAlignment->Center]],
ParametricPlot[Evaluate[{x[t],y[t]}/.DSolve[{x'[t]==y[t],y'[t]==-10x[t],x[0]==1,y[0]==0},{x[t],y[t]},t][[1]]],{t,0,2},PlotRange->All,PlotStyle->Red,AspectRatio->1,
AxesLabel->{x,""},PlotLabel->TextCell[Style["simple harmonic oscillator",Italic],PageWidth->100,TextAlignment->Center]],
ParametricPlot[Evaluate[{x[t],y[t]}/.NDSolve[{x'[t]==y[t],y'[t]==-.26Sin[x[t]],x[0]==0,y[0]==1},{x[t],y[t]},{t,0,30}][[1]]],{t,0,30},PlotRange->All,PlotStyle->Red,
AxesLabel->{x,""},PlotLabel->TextCell[Style["pendulum",Italic],PageWidth->100,TextAlignment->Center]]
},Alignment->Center,Spacings->{{-100,-120,-70}}]