Harmonic Oscillations - Two Dimensions

Manipulate[
ParametricPlot[
{1 Cos[1 *t-ϕ],0.5 Cos[1 *t-δ]},{t,0,temp},
PlotRange->{{-1.05,1.05},{-1.05,1.05}},
PlotStyle->{Blue,AbsoluteThickness[3]},
Frame->False,
Ticks->{{{-1,"-1"},{-0.75,""},{-0.5,""},{-0.25,""},{0,""},{0.25,""},{0.5,""},{0.75,""},{1,"1"}},{{-1,"-1"},{-0.75,""},{-0.5,""},{-0.25,""},{0,""},{0.25,""},{0.5,""},{0.75,""},{1,"1"}}},
GridLines->{{-1.0, -0.75, -0.5, -0.25,0, 0.25,0.5, 0.75, 1.0},{-1.0, -0.75, -0.5, -0.25,0, 0.25,0.5, 0.75, 1.0}},
GridLinesStyle->Directive[LightBlue,AbsoluteThickness[1.3]],
AxesLabel->{Row[{Style["x",Italic]," (cm)"}],Row[{Style["y",Italic]," (cm)"}]},
PerformanceGoal->"Quality",
Epilog->{PointSize[0.02],Point[{1 Cos[1*temp-ϕ],0.5 Cos[1*temp-δ]}]},
ImageSize->400,
LabelStyle->({FontSize->12,FontFamily->"Times"})
],
Style["horizontal",Bold],
{{ϕ,0,"(Subscript[δ, x])"},-π,π,(π/4),ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["vertical",Bold],
{{δ,0,"(Subscript[δ, y])"},-π,π,(π/4),ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
{{temp,0.001,"run"},0.0001,Infinity,ControlType->Trigger}, ControlPlacement->Left]