dg.differential geometry - Harmonic maps in the cotangent bundle

$M$ is a Riemannian manifold with metric $g$ and we have a map $F: M to T^{*}M$ with $F(p)=(p,f(p))$ with a 1-form $f$. On $T^{*}M$ we use the Sasaki-metric.

How can I prove or it is wrong?:

$F$ is harmonic iff $f$ is harmonic.

Thank you and best regards.