2+2

4

Clear[z,v,given,sol,eq1,eq2,diffequ,vplot,yplot,y,t,phaseplot,ta]

diffequ=y''[t]+y[t]

     y[t] + y''[t]

sol=NDSolve[{diffequ==0,y[0]==2, y'[0]==0},y,{t,0,10}]

     {{y -> InterpolatingFunction[{{0., 10.}}, <>]}}

yplot=Plot[y[t]/.sol,{t,0,6.3},PlotStyle->RGBColor[0,0,1]];

vplot=Plot[y'[t]/.sol,{t,0,6.3},PlotStyle->RGBColor[0,1,1]];

xx[ta_]=1Sin[ta];
yy[ta_]=.2 Cos[ta];

p[ta_]={xx[ta],yy[ta]}

     {Sin[ta], 0.2 Cos[ta]}

c=ParametricPlot[{p[ta]},{ta,0,2Pi},AspectRatio->Automatic,
		Compiled->False,Axes->True,
		PlotStyle->{{Thickness[0.01],RGBColor[1,0,0]}}];

Clear[pp,cont]

cont=	 Epilog->{{Text["y[t] = ",{1.8,2.4}]},{Text[y[t].05/.sol[[1]],{3.6,2.4}]},{Text["v[t] = ",{5.8,2.4}]},{Text[y'[t]/.sol[[1]],{7.5,2.4}]}}

     Epilog -> {{Text[y[t] = , {1.8, 2.4}]}, 
      
        {Text[0.05 InterpolatingFunction[{{0., 10.}}, <>][t], {3.6, 2.4}]}, 
      
        {Text[v[t] = , {5.8, 2.4}]}, {Text[InterpolatingFunction[{{0., 10.}}, <>][t], 
      
          {7.5, 2.4}]}}

pp=Do[Show[c,vplot,yplot,Graphics[{Text[FontForm["y(t)",{"CourierB",10}],{1.5,1.5}],
					Text[FontForm["v(t)",{"CourierB",10}],{3.5,1.5}],
				PointSize[.03],Point[  {0, y[t]/.sol[[1]] }  ]   ,
				PointSize[0],Point[  {0,y'[t]/.sol[[1]] }  ] ,
				{PointSize[.02],Point[  {t,(y[t])/.sol[[1]]}   ] }  } ] ,
       cont,PlotRange->{{-2,7.6},{-2,2}},
	AxesLabel->{"time","height"},Ticks->{{0,1,2,3,4,5,6},{{-2,-.1},{-1,-.5},{0,0},{1,.5},{2,.1}}}],
		{t,0,6.3,.2}];