  The square lattice with central-force springs on nearest-neighbor bonds is
isostatic. It has a zero mode for each row and column, and it does not support
shear. Using the Coherent Potential Approximation (CPA), we study how the
random addition, with probability $\mathcal{P}=(z-4)/4$ ($z$ = average number
of nearest neighbors), of springs on next-nearest-neighbor ($NNN$) bonds
restores rigidity and affects phonon structure. We find that the CPA effective
$NNN$ spring constant $\tilde{\kappa}_m(\omega)$, equivalent to the complex
shear modulus $G(\omega)$, obeys the scaling relation,
$\tilde{\kappa}_m(\omega) = \kappa_m h(\omega/\omega^*)$, at small
$\mathcal{P}$, where $\kappa_m = \tilde{\kappa}'_m(0)\sim \mathcal{P}^2$ and
$\omega^* \sim \mathcal{P}$, implying that elastic response is nonaffine at
small $\mathcal{P}$ and that plane-wave states are ill-defined beyond the
Ioffe-Regel limit at $\omega\approx \omega^*$. We identify a divergent length
$l^* \sim \mathcal{P}^{-1}$, and we relate these results to jamming.
