> s1:=piecewise(t>0 and t<2*Pi, sin(t));

> s2:=piecewise(t>0 and t<2*Pi, sin(t/2));

> s3:=piecewise(t>Pi/2 and t<3*Pi/2, sin(t-Pi/2));

> plot({s1,s2,s3},t=-Pi..3*Pi);

> f1:=int(exp(-i*w*t)*sin(t),t=0..2*Pi);

> p1:=sqrt(2*(1-cos(2*Pi*w)))/(abs(1-w^2));

> f2:=int(exp(-i*w*t)*sin(t/2),t=0..2*Pi);

> p2:=sqrt(2*(1+cos(2*Pi*w)))/(abs(1/2-2*w^2));

> f3:=int(exp(-i*w*t)*sin(t),t=0..Pi);

> p3:=sqrt(2*(1+cos(Pi*w)))/(abs(1-w^2));

> plot({p1,p2,p3},w=0..5);

>

>