III. System Parameters Disk Mass (ma) Brass Weight Mass (mw) Brass Diameter (dw) Disk Diameter (da) Spring Shaft Length (Ls) Spring Shaft Diameter (d) Spring Shaft Shear Modulus (G) Encoder Resolution 360 g 500 g 5 cm 20 cm 30 cm 3.15 mm 79 GPa 160001 counts/rev IV. Assignments a. Pre-Lab Assignment 1. What is the torsional spring constant of a shaft with diameter d=3.15 mm, Length 1=30 cm, and shear modulus G=79 GPa? 2. What is the natural circular frequency of a system with torsional spring constant k and mass moment of inertia Jo? 3. What is the critical damping constant of a torsional vibration system with mass moment of inertia Jo and natural frequency o? (Remember torsional systems are analogous to translational systems).