> restart;

> w1:=1+cos(t)/4:z1:=t/12-sin(2*t)/24:x1:=k*w1*cos(z1):y1:=k*w1*sin(z1):a1:=animate([x1,y1,t=0..24*Pi],k=0..2,frames=50,numpoints=500,axes=none,scaling=constrained,color=coral):

> with(plots):

> w2:=1+cos(t)/2:z2:=t/6-sin(2*t)/12:x2:=k*w2*cos(z2):y2:=k*w2*sin(z2):a2:=animate([x2,y2,t=0..24*Pi],k=0..1,frames=50,numpoints=500,axes=none,scaling=constrained,color=blue):

> display(a1,a2);

>