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A zero-temperature critical point has been invoked to control the anomalousbehavior of granular matter as it approaches jamming or mechanical arrest.Criticality manifests itself in an anomalous spectrum of low-frequency normalmodes and scaling behavior near the jamming transition. The critical point mayexplain the peculiar mechanical properties of dissimilar systems such asglasses and granular materials. Here, we study the critical scenario via anexperimental measurement of the normal modes frequencies of granular matterunder stress from a pole decomposition analysis of the effective mass. Weextract a complex-valued characteristic frequency which displays scaling$|\omega^*(\sigma)|\sim\sigma^{\Omega'}$ with vanishing stress $\sigma$ for avariety of granular systems. The critical exponent is smaller than thatpredicted by mean-field theory opening new challenges to explain the exponentfor frictional and dissipative granular matter. Our results shed light on theanomalous behavior of stress-dependent acoustics and attenuation in granularmaterials near the jamming transition.

Stress-dependent normal mode frequencies from the effective mass of granular matter