Vectors & Functions

Manipulate[With[{f={Sin[k1*t],Cos[k2*t]+Cos[k3*t]}},
Show[Table[Graphics[{Hue[t/100],
Arrow[{{Sin[t],Cos[t]},
f+{Sin[t],Cos[t]}}]}],
{t,0,100Pi}],ImageSize->{500,500}]],
{k1,Range[1,5,1]},{k2,Range[5,9,1]},{k3,Range[4,8,1]}]