  We report studies, using a two mode torsional oscillator, of the putative
supersolid signature in polycrystalline 4He. Measurements at two frequencies
enable us to eliminate the viscoelastic contribution to the signature, and
other instrumental effects arising from the temperature dependent shear modulus
of the sample. The complex response function of the sample, encoded via its
effective moment of inertia, shows an unexpected and unexplained frequency
dependence. This cannot be accounted for by glassy dynamics within the sample.
The results do not rule out the possibility of supersolidity in bulk solid 4He.
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