  We study the energy distribution of harmonic 1-forms on a compact hyperbolic
Riemann surface $S$ where a short closed geodesic is pinched. If the geodesic
separates the surface into two parts, then the Jacobian torus of $S$ develops
into a torus that splits. If the geodesic is nonseparating then the Jacobian
torus of $S$ degenerates. The aim of this work is to get insight into this
process and give estimates in terms of geometric data of both the initial
surface $S$ and the final surface, such as its injectivity radius and the
lengths of geodesics that form a homology basis. As an invariant we introduce
new families of symplectic matrices that compensate for the lack of full
dimensional Gram-period matrices in the noncompact case.
