The contribution of solid He-4 contained in the torsion rod of a torsional oscillator to its resonant frequency is investigated using a modified torsional oscillator. The purpose of the present study is to discriminate between two possible contributions to the resonant frequency of the torsional oscillator, which abruptly increases below 3 0.2 K. The first possible contribution is the elastic property change of solid He-4 in the torsion rod (i.e., shear modulus increase), and the second possible contribution is mass decoupling by the supersolid transition of solid He-4 in the oscillating body (i.e., a decrease in the momentum inertia). A torsional oscillator that has no hollow space for solid He-4 in the body was constructed, and its resonant frequency and Q-factor were compared to those of the conventional oscillator. The shear modulus contributions of solid He-4 in the torsion rod were identical, but the momentum inertias of solid He-4 in the oscillating body were quite different between the two oscillators. Surprisingly, the observed frequency behavior and magnitude of the two oscillators were comparable. This finding indicates that the resonant frequency increase observed in the torsional oscillator originates from the increase in the shear modulus of solid He-4 in the torsion rod, rather than from the momentum inertia decrease of the solid He-4 in the oscillating body. The temperature dependence of the increase in the shear modulus of solid He-4 was well reproduced by the dislocation-vibration model with a much lower He-3 impurity concentration than that of commercially available He-4 gas.