restart: with(plots):harmo_euler := proc(t0,x0,v0,h,n,x,v,t) local i; x[0] := x0; v[0] := v0; t[0] := t0; for i to n do t[i]:=t[i-1]+h; x[i]:=x[i-1]+h*v[i-1]; v[i]:=v[i-1]-h*x[i-1]; od; end;harmo_runge := proc(t0,x0,v0,h,n,x,v,t) local i; x[0] := x0; v[0] := v0; t[0] := t0; for i to n do t[i]:=t[i-1]+h; x[i]:=x[i-1]+h*(v[i-1]-h/2*x[i-1]); v[i]:=v[i-1]-h*(x[i-1]+h/2*v[i-1]); od; end;

Warning, the name changecoords has been redefined

NiM+SSxoYXJtb19ldWxlckc2ImYqNipJI3QwR0YlSSN4MEdGJUkjdjBHRiVJImhHRiVJIm5HRiVJInhHRiVJInZHRiVJInRHRiU2I0kiaUdGJUYlRiVDJj4mOSk2IyIiITklPiY5KkY2OSY+JjkrRjY5JD8oOCQiIiJGQzkoSSV0cnVlR0kqcHJvdGVjdGVkR0ZGQyU+JkY/NiNGQiwmJkY/NiMsJkZCRkMhIiJGQ0ZDOSdGQz4mRjVGSiwmJkY1Rk1GQyomRlBGQyZGO0ZNRkNGQz4mRjtGSiwmRlZGQyomRlBGQ0ZURkNGT0YlRiVGJQ==NiM+SSxoYXJtb19ydW5nZUc2ImYqNipJI3QwR0YlSSN4MEdGJUkjdjBHRiVJImhHRiVJIm5HRiVJInhHRiVJInZHRiVJInRHRiU2I0kiaUdGJUYlRiVDJj4mOSk2IyIiITklPiY5KkY2OSY+JjkrRjY5JD8oOCQiIiJGQzkoSSV0cnVlR0kqcHJvdGVjdGVkR0ZGQyU+JkY/NiNGQiwmJkY/NiMsJkZCRkMhIiJGQ0ZDOSdGQz4mRjVGSiwmJkY1Rk1GQyomRlBGQywmJkY7Rk1GQyomRlBGQ0ZURkMjRk8iIiNGQ0ZDPiZGO0ZKLCZGV0ZDKiZGUEZDLCZGVEZDKiZGUEZDRldGQyNGQ0ZaRkNGT0YlRiVGJQ==

harmo_euler(0,1,0,.126,50,x50,v50,t50); harmo_euler(0,1,0,.0126,500,x500,v500,t500); harmo_runge(0,1,0,.126,50,xr50,vr50,tr50); harmo_runge(0,1,0,.0126,500,xr500,vr500,tr500);

NiMkIiprJUcuQyEjNQ==NiMkIStSKHpaciIhIzY=NiMkISowNF5NJCEjNQ==NiMkIStKJmYhKXAiISM2

plot([[seq([t50[j],x50[j]],j=1..50)],[seq([t500[j*5],x500[j*5]],j=1..100)],[seq([t50[j],v50[j]],j=1..50)],[seq([t500[j*5],v500[j*5]],j=1..100)],cos(x),-sin(x)],x=0..2*Pi,y=-1.5..1.5,style=[point,point,point,point,line,line],color=[red,red,blue,blue,red,blue],resolution=1000,symbol=point);plot([[seq([tr50[j],xr50[j]],j=1..50)],[seq([tr500[j*5],xr500[j*5]],j=1..100)],[seq([tr50[j],vr50[j]],j=1..50)],[seq([tr500[j*5],vr500[j*5]],j=1..100)],cos(x),-sin(x)],x=0..2*Pi,y=-1.5..1.5,style=[point,point,point,point,line,line],color=[red,red,blue,blue,red,blue],resolution=1000,symbol=point);pendel := proc(t0,x0,v0,h,n,x,v,t) local i; x[0] := x0; v[0] := v0; t[0] := t0; for i to n do t[i]:=t[i-1]+h; x[i]:=x[i-1]+h*(v[i-1] -h/2*sin(x[i-1])); v[i]:=v[i-1]-h*sin(x[i-1]+h/2*v[i-1]); od; end;

NiM+SSdwZW5kZWxHNiJmKjYqSSN0MEdGJUkjeDBHRiVJI3YwR0YlSSJoR0YlSSJuR0YlSSJ4R0YlSSJ2R0YlSSJ0R0YlNiNJImlHRiVGJUYlQyY+JjkpNiMiIiE5JT4mOSpGNjkmPiY5K0Y2OSQ/KDgkIiIiRkM5KEkldHJ1ZUdJKnByb3RlY3RlZEdGRkMlPiZGPzYjRkIsJiZGPzYjLCZGQkZDISIiRkNGQzknRkM+JkY1RkosJiZGNUZNRkMqJkZQRkMsJiZGO0ZNRkMqJkZQRkMtSSRzaW5HNiRGRkkoX3N5c2xpYkdGJTYjRlRGQyNGTyIiI0ZDRkM+JkY7RkosJkZXRkMqJkZQRkMtRlo2IywmRlRGQyomRlBGQ0ZXRkMjRkNGaW5GQ0ZPRiVGJUYl

harmo_euler(0,0.1,0,.0126,500,xa1,va1,ta1); harmo_euler(0,0.6,0,.0126,500,xa2,va2,ta2); harmo_euler(0,1.1,0,.0126,500,xa3,va3,ta3); harmo_euler(0,0.6,0,.0126,500,xa4,va4,ta4); harmo_euler(0,2.1,0,.0126,500,xa5,va5,ta5); harmo_euler(0,0.6,0,.0126,500,xa6,va6,ta6); harmo_euler(0,3.1,0,.0126,500,xa7,va7,ta7);

NiMkIStSKHpaciIhIzc=NiMkIStveicpRzUhIzY=NiMkIStdd0QnKT0hIzY=NiMkIStveicpRzUhIzY=NiMkIStXcy4sTyEjNg==NiMkIStveicpRzUhIzY=NiMkIStpdCJlSiYhIzY=

plot([ [seq([ta1[j],xa1[j]],j=1..500)], [seq([ta2[j],xa2[j]],j=1..500)], [seq([ta3[j],xa3[j]],j=1..500)], [seq([ta4[j],xa4[j]],j=1..500)], [seq([ta5[j],xa5[j]],j=1..500)], [seq([ta6[j],xa6[j]],j=1..500)], [seq([ta7[j],xa7[j]],j=1..500)] ],style=point,color=blue,resolution=1000,symbol=point);pendelarray := proc(start,steps,diff,xges,vges,tges) local i,curr; curr:=start; for i to steps do pendel(0,curr,0,.0126,1000,xges[i],yges[i],tges[i]); curr:=curr+diff; od; end;

NiM+SSxwZW5kZWxhcnJheUc2ImYqNihJJnN0YXJ0R0YlSSZzdGVwc0dGJUklZGlmZkdJKnByb3RlY3RlZEdGK0kleGdlc0dGJUkldmdlc0dGJUkldGdlc0dGJTYkSSJpR0YlSSVjdXJyR0YlRiVGJUMkPjglOSQ/KDgkIiIiRjg5JUkldHJ1ZUdGK0MkLUkncGVuZGVsR0YlNioiIiFGNEY/JCIkRSIhIiUiJSs1JjknNiNGNyZJJXlnZXNHRiVGRiY5KUZGPkY0LCZGNEY4OSZGOEYlRiVGJQ==

pendelarray(0.1,120,.025,xges,vges,tges);

NiMkIiUrSiEiJA==

display(seq(plot([[seq([tges[1][j],xges[a][j]],j=1..1000)],(0.1+a*.025)*cos(x)],x=0..4*Pi,style=line,color=[blue,red],thickness=[2,1],resolution=2000,symbol=point,scaling=CONSTRAINED),a=1..120),insequence=true);display(seq(plot([[seq([tges[1][j],xges[a][j]],j=1..1000)],(0.1+a*.025)*cos(x)],x=0..4*Pi,style=line,color=[blue,red],thickness=[2,1],resolution=3000,symbol=point,scaling=CONSTRAINED,labels=["t","x(t)"],title="Pendel: Vergleich von allgemeiner L\366sung und Spezialfall mit harmonischer Schwingung",transparency=1,titlefont=[Helvetica,BOLD,12],labeldirections=[horizontal,vertical],axesfont=[Helvetica,normal,10],labelfont=[Helvetica,normal,10]),a=1..120),insequence=true);