Decoupling NCRI from shear modulus changes in solid $^4$He*

Day and Beamish report a significant increase in the shear modulus of solid $^4$He [1] below 250 mK with temperature dependence similar to the non-classical rotational inertia (NCRI) response seen in torsional oscillator measurements [2]. Finite element calculations show that stiffening of the solid $^4$He could mimic very small NCRI signals [3]. We have constructed a one-piece, welded oscillator which is designed to minimize the effect from stiffening of the solid helium. Preliminary data will be presented. \newline [1] J. Day and J. R. Beamish, arXiv:0709.4666v1 (2007). \newline [2] E. Kim and M. H. W. Chan, Science \textbf{305}, 1941 (2004). \newline [3] A. C. Clark and M. H. W. arXiv:0711.3619v1 (2007).