  We obtain a sharp estimate for the best constant $C>0$ in the Wirtinger type
inequality \[ \int_0^{2\pi}\gamma^pw^2\le C\int_0^{2\pi}\gamma^qw'^2 \] where
$\gamma$ is bounded above and below away from zero, $w$ is $2\pi$-periodic and
such that $\int_0^{2\pi}\gamma^pw=0$, and $p+q\ge0$. Our result generalizes an
inequality of Piccinini and Spagnolo.
