  Like other critical phenomena, the jamming transition accompanies the
divergence of the relaxation time $\tau$. A recent numerical study of
frictionless spherical particles proves that $\tau$ is inversely proportional
to the lowest non-zero eigenvalue $\lambda_1$ of the dynamical matrix. In this
note, we derive the scaling of $\lambda_1$ below the jamming transition point
$\varphi_J$ by solving the linearized dynamical equation. The resultant
critical exponent agrees with a previous theoretical result for sheared
suspension obtained by applying the virtual work theorem to a simple shear,
highlighting the universality of the relaxation dynamics below jamming.
