Accurate determination of the complex shear modulus of soft tissues and soft-tissue-like materials in the 10-300 Hz frequency range is very important to researchers in MR elastography and acoustic radiation force impulse (ARFI) imaging. A variety of instruments for making such measurements has been reported, but none of them is easily reproduced, and none have been tested to conform to causality via the Kramers-Kronig (K-K) relations. A promising linear oscillation instrument described in a previous brief report operates between 20 and 160 Hz, but results were not tested for conformity to the K-K relations. We have produced a similar instrument with our own version of the electronic components and have also accounted for instrumental effects on the data reduction, which is not addressed in the previous report. The improved instrument has been shown to conform to an accurate approximation of the K-K relations over the 10-300 Hz range. The K-K approximation is based on the Weichert mechanical circuit model. We also found that the sample thickness must be small enough to obtain agreement with a calibrated commercial rheometer. A complete description of the improved instrument is given, facilitating replication in other labs.