  The square and kagome lattices with nearest neighbor springs of spring
constant $k$ are isostatic with a number of zero-frequency modes that scale
with their perimeter. We analytically study the approach to this isostatic
limit as the spring constant $k'$ for next-nearest-neighbor bonds vanishes. We
identify a characteristic frequency $\omega^* \sim \sqrt{k'}$ and length $l^*
\sim \sqrt{k/k'}$ for both lattices. The shear modulus $C_{44}= k'$ of the
square lattice vanishes with $k'$, but that for the kagome lattice does not.
